2004-03-03 21:24:06 +01:00
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#include "stdafx.h"
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#include "defs.h"
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extern void test_abs(void);
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extern void test_arccos(void);
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extern void test_arccosh(void);
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extern void test_arcsin(void);
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extern void test_arcsinh(void);
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extern void test_arctan(void);
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extern void test_arctanh(void);
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2005-07-30 21:37:29 +02:00
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extern void test_besselj(void);
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extern void test_bessely(void);
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extern void test_carac(void);
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2004-03-03 21:24:06 +01:00
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extern void test_ceiling(void);
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extern void test_charpoly(void);
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extern void test_coeff(void);
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extern void test_condense(void);
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2004-08-15 21:30:02 +02:00
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extern void test_contract(void);
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2005-07-30 21:37:29 +02:00
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extern void test_convolution(void);
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2004-03-03 21:24:06 +01:00
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extern void test_cos(void);
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extern void test_cosh(void);
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2005-06-25 21:29:07 +02:00
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extern void test_denominator(void);
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2004-03-03 21:24:06 +01:00
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extern void test_derivative(void);
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2005-07-30 21:37:29 +02:00
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extern void test_dirac(void);
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2004-03-03 21:24:06 +01:00
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extern void test_display(void);
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extern void test_divisors(void);
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extern void test_eigen(void);
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2005-07-30 21:37:29 +02:00
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extern void test_erf(void);
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extern void test_erfc(void);
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2004-06-18 01:02:29 +02:00
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extern void test_expcos(void);
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extern void test_expsin(void);
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2004-03-03 21:24:06 +01:00
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extern void test_factor_number(void);
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extern void test_factorpoly(void);
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extern void test_for(void);
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extern void test_floor(void);
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2005-07-30 21:37:29 +02:00
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extern void test_fourier(void);
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extern void test_gamma(void);
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extern void test_heaviside(void);
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2004-03-03 21:24:06 +01:00
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extern void test_index(void);
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2004-06-12 03:12:13 +02:00
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extern void test_inner(void);
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2004-03-03 21:24:06 +01:00
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extern void test_integral(void);
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extern void test_isprime(void);
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extern void test_lcm(void);
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2004-07-16 02:36:18 +02:00
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extern void test_log(void);
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2004-03-03 21:24:06 +01:00
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extern void test_madd(void);
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extern void test_mdiv(void);
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extern void test_mgcd(void);
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extern void test_mmod(void);
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extern void test_mmul(void);
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extern void test_mod(void);
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extern void test_mpow(void);
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extern void test_mprime(void);
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extern void test_mroot(void);
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extern void test_msub(void);
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extern void test_multiply(void);
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2005-06-25 21:29:07 +02:00
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extern void test_numerator(void);
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2004-06-12 02:40:07 +02:00
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extern void test_outer(void);
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2004-03-03 21:24:06 +01:00
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extern void test_power(void);
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extern void test_product(void);
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extern void test_prog(void);
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extern void test_rationalize(void);
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extern void test_roots(void);
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extern void test_scan(void);
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extern void test_simplify(void);
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2005-07-30 21:37:29 +02:00
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extern void test_sgn(void);
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2004-03-03 21:24:06 +01:00
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extern void test_sin(void);
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extern void test_sinh(void);
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extern void test_sum(void);
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extern void test_tan(void);
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extern void test_tanh(void);
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extern void test_taylor(void);
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2005-07-30 21:37:29 +02:00
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extern void test_tchebychevT(void);
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extern void test_tchebychevU(void);
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2004-03-03 21:24:06 +01:00
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extern void test_tensor(void);
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extern void test_test(void);
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extern void test_trace(void);
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2004-08-15 21:30:02 +02:00
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extern void test_transpose(void);
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2004-03-03 21:24:06 +01:00
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extern void test_user_func(void);
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extern void test_wedge(void);
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2004-08-15 21:30:02 +02:00
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extern void test_zero(void);
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2004-03-03 21:24:06 +01:00
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char logbuf[1000];
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static FILE *logfile;
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static jmp_buf jbuf;
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void
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selftest(void)
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{
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#if 0 // don't use log file
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#ifdef MAC
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static char buf[144];
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strcpy(buf, getenv("HOME"));
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strcat(buf, "/Desktop/Eigenmath.out");
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logfile = fopen(buf, "w");
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#else
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logfile = fopen("selftest.txt", "w");
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#endif
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#endif
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if (setjmp(jbuf))
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return;
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// test bignum arithmetic
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test_madd();
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test_msub();
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test_mmul();
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test_mdiv();
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test_mmod();
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test_mprime();
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test_quickfactor();
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test_mgcd();
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test_mpow();
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test_mroot();
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test_multiply();
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test_scan();
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test_power();
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test_factor_number();
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test_test();
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test_all();
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test_user_func();
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test_tensor();
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test_abs();
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2005-07-30 21:37:29 +02:00
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test_besselj();
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test_bessely();
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test_carac();
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2004-03-03 21:24:06 +01:00
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test_ceiling();
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test_charpoly();
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test_condense();
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2004-08-15 21:30:02 +02:00
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test_contract();
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2005-07-30 21:37:29 +02:00
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test_convolution();
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2005-06-25 21:29:07 +02:00
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test_denominator();
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2004-03-03 21:24:06 +01:00
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test_derivative();
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2005-07-30 21:37:29 +02:00
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test_dirac();
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test_erf();
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test_erfc();
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2004-06-18 01:02:29 +02:00
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test_expcos();
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test_expsin();
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2004-03-03 21:24:06 +01:00
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test_gcd();
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test_factorpoly();
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test_floor();
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test_for();
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2005-07-30 21:37:29 +02:00
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test_fourier();
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test_gamma();
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2004-06-12 03:12:13 +02:00
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test_inner();
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2004-03-03 21:24:06 +01:00
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test_lcm();
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2004-07-16 02:36:18 +02:00
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test_log();
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2004-03-03 21:24:06 +01:00
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test_mod();
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2005-06-25 21:29:07 +02:00
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test_numerator();
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2004-06-12 02:40:07 +02:00
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test_outer();
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2004-03-03 21:24:06 +01:00
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test_product();
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test_prog();
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test_rationalize();
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2005-07-30 21:37:29 +02:00
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test_sgn();
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2004-03-03 21:24:06 +01:00
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test_sum();
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test_taylor();
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2005-07-30 21:37:29 +02:00
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test_tchebychevT();
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test_tchebychevU();
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2004-03-03 21:24:06 +01:00
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test_trace();
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2004-08-15 21:30:02 +02:00
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test_transpose();
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test_zero();
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2004-03-03 21:24:06 +01:00
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test_hermite();
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test_laguerre();
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test_legendre();
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test_binomial();
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test_divisors();
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test_coeff();
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test_sin();
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test_cos();
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test_tan();
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test_sinh();
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test_cosh();
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test_tanh();
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test_arcsin();
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test_arcsinh();
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test_arccos();
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test_arccosh();
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test_arctan();
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test_arctanh();
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test_wedge();
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test_index();
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test_isprime();
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test_integral();
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test_simplify();
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test_roots();
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test_eigen();
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logout("OK, all tests passed.\n");
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if (logfile)
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fclose(logfile);
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}
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void
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logout(char *s)
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{
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printstr(s);
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2004-05-28 20:08:11 +02:00
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// if (logfile)
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// fprintf(logfile, "%s", s);
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2004-03-03 21:24:06 +01:00
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}
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void
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errout(void)
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{
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logout("\n");
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2004-05-28 20:08:11 +02:00
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// if (logfile)
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// fclose(logfile);
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2004-03-03 21:24:06 +01:00
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longjmp(jbuf, 1);
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}
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2005-08-07 16:42:42 +02:00
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int test_flag;
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extern int out_count;
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extern void run(char *);
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char *script[] = {
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"2/3",
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"2/3",
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"2.0/3",
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"0.666667",
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"2/3.0",
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"0.666667",
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"2.0/3.0",
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"0.666667",
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"-2.0/3.0",
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"-0.666667",
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// symbols
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"a=quote(a)",
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"a",
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"b=quote(b)",
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"b",
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"c=quote(c)",
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"c",
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"d=quote(d)",
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"d",
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// scanner
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"a 5", // 2nd factor is T_INTEGER
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"5*a",
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"a 5.0", // 2nd factor is T_DOUBLE
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"5*a",
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// "a \"hello\"", // 2nd factor is T_STRING
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// "\"hello\"*a",
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// print format
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"2*1/a",
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"2/a",
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"-1/a",
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"-1/a",
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"a/b",
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"a/b",
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//
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"2^(1/2)",
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"2^(1/2)",
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"r*exp(i*phi)", // sort order (see ~e in misc.c)
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"r*exp(i*phi)",
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// string arguments are printed with quotes
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// "quote(print(a,\" \",b))",
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// "print(a,\" \",b)",
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// "float(2/3)",
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// "0.666667",
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/* from yacas to do list */
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"2380105039001857 * 1260448573",
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"3000000000000000000000061",
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// floating point
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"A=float(1000!)",
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"",
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#if 0
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#ifdef MAC
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"A",
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"Inf",
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"A-A",
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"NaN",
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"A/A",
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"NaN",
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#else
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"A",
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"inf",
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"A-A",
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"nan",
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"A/A",
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"nan",
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#endif
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#endif
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"A=quote(A)",
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"",
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// divide by zero
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"1/0",
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"Stop: divide by zero",
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"1.0/0.0",
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"Stop: divide by zero",
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/* sum */
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"0+0",
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"0",
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"0+a",
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"a",
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"a+0",
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"a",
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|
|
|
|
|
|
|
|
"0+(a+b)",
|
|
|
|
|
"a+b",
|
|
|
|
|
|
|
|
|
|
"(a+b)+0",
|
|
|
|
|
"a+b",
|
|
|
|
|
|
|
|
|
|
"1+2",
|
|
|
|
|
"3",
|
|
|
|
|
|
|
|
|
|
"a+0",
|
|
|
|
|
"a",
|
|
|
|
|
|
|
|
|
|
"0+a",
|
|
|
|
|
"a",
|
|
|
|
|
|
|
|
|
|
"a+a",
|
|
|
|
|
"2*a",
|
|
|
|
|
|
|
|
|
|
"a+2*a",
|
|
|
|
|
"3*a",
|
|
|
|
|
|
|
|
|
|
"2*a+a",
|
|
|
|
|
"3*a",
|
|
|
|
|
|
|
|
|
|
"2*a+3*a",
|
|
|
|
|
"5*a",
|
|
|
|
|
|
|
|
|
|
"a*b+a*b",
|
|
|
|
|
"2*a*b",
|
|
|
|
|
|
|
|
|
|
"a*b+2*a*b",
|
|
|
|
|
"3*a*b",
|
|
|
|
|
|
|
|
|
|
"2*a*b+a*b",
|
|
|
|
|
"3*a*b",
|
|
|
|
|
|
|
|
|
|
"2*a*b+3*a*b",
|
|
|
|
|
"5*a*b",
|
|
|
|
|
|
|
|
|
|
"1/2*a+1/2*a",
|
|
|
|
|
"a",
|
|
|
|
|
|
|
|
|
|
"1/2*a*b+1/2*a*b",
|
|
|
|
|
"a*b",
|
|
|
|
|
|
|
|
|
|
"a+a+a",
|
|
|
|
|
"3*a",
|
|
|
|
|
|
|
|
|
|
"a+b+b",
|
|
|
|
|
"a+2*b",
|
|
|
|
|
|
|
|
|
|
"2*a+2*a",
|
|
|
|
|
"4*a",
|
|
|
|
|
|
|
|
|
|
"1/4*a-1/4*a",
|
|
|
|
|
"0",
|
|
|
|
|
|
|
|
|
|
"(a+b+c+d)-(a+b+c+d)",
|
|
|
|
|
"0",
|
|
|
|
|
|
|
|
|
|
/* power */
|
|
|
|
|
|
|
|
|
|
"0^0", // see ross' book, p. 129
|
|
|
|
|
"1",
|
|
|
|
|
|
|
|
|
|
"a^0",
|
|
|
|
|
"1",
|
|
|
|
|
|
|
|
|
|
"a^1",
|
|
|
|
|
"a",
|
|
|
|
|
|
|
|
|
|
"1^a",
|
|
|
|
|
"1",
|
|
|
|
|
|
|
|
|
|
"a^a",
|
|
|
|
|
"a^a",
|
|
|
|
|
|
|
|
|
|
"2^(1/2)",
|
|
|
|
|
"2^(1/2)",
|
|
|
|
|
|
|
|
|
|
// "a^(b+c)",
|
|
|
|
|
// "a^b*a^c",
|
|
|
|
|
|
|
|
|
|
// "a^(b+c+d)",
|
|
|
|
|
// "a^b*a^c*a^d",
|
|
|
|
|
|
|
|
|
|
"(a*b)^c",
|
|
|
|
|
"a^c*b^c",
|
|
|
|
|
|
|
|
|
|
"(a*b*c)^d",
|
|
|
|
|
"a^d*b^d*c^d",
|
|
|
|
|
|
|
|
|
|
"2^3",
|
|
|
|
|
"8",
|
|
|
|
|
|
|
|
|
|
"a^(2*a)",
|
|
|
|
|
"a^(2*a)",
|
|
|
|
|
|
|
|
|
|
"a^(2*a*b)",
|
|
|
|
|
"a^(2*a*b)",
|
|
|
|
|
|
|
|
|
|
"(a^2)^3",
|
|
|
|
|
"a^6",
|
|
|
|
|
|
|
|
|
|
"a^2^3",
|
|
|
|
|
"a^8",
|
|
|
|
|
/*
|
|
|
|
|
"12^(1/2)",
|
|
|
|
|
"2*3^(1/2)",
|
|
|
|
|
|
|
|
|
|
"12^(-1/2)",
|
|
|
|
|
"1/2*(1/3)^(1/2)",
|
|
|
|
|
|
|
|
|
|
"8^(2/3)",
|
|
|
|
|
"4",
|
|
|
|
|
|
|
|
|
|
"8^(-2/3)",
|
|
|
|
|
"1/4",
|
|
|
|
|
|
|
|
|
|
"2^(3/2)",
|
|
|
|
|
"2*2^(1/2)",
|
|
|
|
|
|
|
|
|
|
"(3/2)^(-1/2)",
|
|
|
|
|
"(2/3)^(1/2)",
|
|
|
|
|
|
|
|
|
|
"(3/4)^(1/2)",
|
|
|
|
|
"1/2*3^(1/2)",
|
|
|
|
|
|
|
|
|
|
"(9/4)^(1/2)",
|
|
|
|
|
"3/2",
|
|
|
|
|
|
|
|
|
|
"(9/4)^(3/2)",
|
|
|
|
|
"27/8",
|
|
|
|
|
|
|
|
|
|
"3*3^(-1/2)",
|
|
|
|
|
"3^(1/2)",
|
|
|
|
|
*/
|
|
|
|
|
"(a^b)^c",
|
|
|
|
|
"a^(b*c)",
|
|
|
|
|
|
|
|
|
|
"((a+b)^(-2))^(-1)",
|
|
|
|
|
// "a^2+b^2+2*a*b",
|
|
|
|
|
"2*a*b+a^2+b^2",
|
|
|
|
|
|
|
|
|
|
#if 0
|
|
|
|
|
"(-27)^(1/3)",
|
|
|
|
|
"-3",
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
// make sure scanner doesn't produce imaginary
|
|
|
|
|
|
|
|
|
|
"quote((-a/b)^(1/2))",
|
|
|
|
|
"(-a/b)^(1/2)",
|
|
|
|
|
|
|
|
|
|
#if 0
|
|
|
|
|
|
|
|
|
|
/* roots of large numbers */
|
|
|
|
|
|
|
|
|
|
"x=10^20",
|
|
|
|
|
"x",
|
|
|
|
|
|
|
|
|
|
"x^(1/2)",
|
|
|
|
|
"10000000000",
|
|
|
|
|
|
|
|
|
|
"x^(-1/2)",
|
|
|
|
|
"1/10000000000",
|
|
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
//
|
|
|
|
|
// arctan
|
|
|
|
|
//
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
|
|
#if 0
|
|
|
|
|
|
|
|
|
|
/* arctan2 */
|
|
|
|
|
|
|
|
|
|
"arctan2(0,0)",
|
|
|
|
|
"0",
|
|
|
|
|
|
|
|
|
|
"arctan2(0,1)",
|
|
|
|
|
"0",
|
|
|
|
|
|
|
|
|
|
"arctan2(0,-1)",
|
|
|
|
|
"pi",
|
|
|
|
|
|
|
|
|
|
"arctan2(1,0)",
|
|
|
|
|
"1/2*pi",
|
|
|
|
|
|
|
|
|
|
"arctan2(-1,0)",
|
|
|
|
|
"-1/2*pi",
|
|
|
|
|
|
|
|
|
|
/* sin */
|
|
|
|
|
|
|
|
|
|
"sin(-pi)", // -180 degrees
|
|
|
|
|
"0",
|
|
|
|
|
|
|
|
|
|
"sin(-pi*5/6)", // -150 degrees
|
|
|
|
|
"-1/2",
|
|
|
|
|
|
|
|
|
|
"sin(-3*pi/4)", // -135 degrees
|
|
|
|
|
"-1/2*2^(1/2)",
|
|
|
|
|
|
|
|
|
|
"sin(-2*pi/3)", // -120 degrees
|
|
|
|
|
"-1/2*3^(1/2)",
|
|
|
|
|
|
|
|
|
|
"sin(-pi/2)", // -90 degrees
|
|
|
|
|
"-1",
|
|
|
|
|
|
|
|
|
|
"sin(-pi/3)", // -60 degrees
|
|
|
|
|
"-1/2*3^(1/2)",
|
|
|
|
|
|
|
|
|
|
"sin(-pi/4)", // -45 degrees
|
|
|
|
|
"-1/2*2^(1/2)",
|
|
|
|
|
|
|
|
|
|
"sin(-pi/6)", // -30 degrees
|
|
|
|
|
"-1/2",
|
|
|
|
|
|
|
|
|
|
"sin(0)", // 0 degrees
|
|
|
|
|
"0",
|
|
|
|
|
|
|
|
|
|
"sin(pi/6)", // 30 degrees
|
|
|
|
|
"1/2",
|
|
|
|
|
|
|
|
|
|
"sin(pi/4)", // 45 degrees
|
|
|
|
|
"1/2*2^(1/2)",
|
|
|
|
|
|
|
|
|
|
"sin(pi/3)", // 60 degrees
|
|
|
|
|
"1/2*3^(1/2)",
|
|
|
|
|
|
|
|
|
|
"sin(pi/2)", // 90 degrees
|
|
|
|
|
"1",
|
|
|
|
|
|
|
|
|
|
"sin(2*pi/3)", // 120 degrees
|
|
|
|
|
"1/2*3^(1/2)",
|
|
|
|
|
|
|
|
|
|
"sin(3*pi/4)", // 135 degrees
|
|
|
|
|
"1/2*2^(1/2)",
|
|
|
|
|
|
|
|
|
|
"sin(pi*5/6)", // 150 degrees
|
|
|
|
|
"1/2",
|
|
|
|
|
|
|
|
|
|
"sin(pi)", // 180 degrees
|
|
|
|
|
"0",
|
|
|
|
|
|
|
|
|
|
"sin(pi*7/6)", // 210 degrees
|
|
|
|
|
"-1/2",
|
|
|
|
|
|
|
|
|
|
/* cos */
|
|
|
|
|
|
|
|
|
|
"cos(-pi)", // -180 degrees
|
|
|
|
|
"-1",
|
|
|
|
|
|
|
|
|
|
"cos(-pi*5/6)", // -150 degrees
|
|
|
|
|
"-1/2*3^(1/2)",
|
|
|
|
|
|
|
|
|
|
"cos(-pi*3/4)", // -135 degrees
|
|
|
|
|
"-1/2*2^(1/2)",
|
|
|
|
|
|
|
|
|
|
"cos(-pi*2/3)", // -120 degrees
|
|
|
|
|
"-1/2",
|
|
|
|
|
|
|
|
|
|
"cos(-pi/2)", // -90 degrees
|
|
|
|
|
"0",
|
|
|
|
|
|
|
|
|
|
"cos(-pi/3)", // -60 degrees
|
|
|
|
|
"1/2",
|
|
|
|
|
|
|
|
|
|
"cos(-pi/4)", // -45 degrees
|
|
|
|
|
"1/2*2^(1/2)",
|
|
|
|
|
|
|
|
|
|
"cos(-pi/6)", // -30 degrees
|
|
|
|
|
"1/2*3^(1/2)",
|
|
|
|
|
|
|
|
|
|
"cos(0)", // 0 degrees
|
|
|
|
|
"1",
|
|
|
|
|
|
|
|
|
|
"cos(pi/6)", // 30 degrees
|
|
|
|
|
"1/2*3^(1/2)",
|
|
|
|
|
|
|
|
|
|
"cos(pi/4)", // 45 degrees
|
|
|
|
|
"1/2*2^(1/2)",
|
|
|
|
|
|
|
|
|
|
"cos(pi/3)", // 60 degrees
|
|
|
|
|
"1/2",
|
|
|
|
|
|
|
|
|
|
"cos(pi/2)", // 90 degrees
|
|
|
|
|
"0",
|
|
|
|
|
|
|
|
|
|
"cos(pi*2/3)", // 120 degrees
|
|
|
|
|
"-1/2",
|
|
|
|
|
|
|
|
|
|
"cos(pi*3/4)", // 135 degrees
|
|
|
|
|
"-1/2*2^(1/2)",
|
|
|
|
|
|
|
|
|
|
"cos(pi*5/6)", // 150 degrees
|
|
|
|
|
"-1/2*3^(1/2)",
|
|
|
|
|
|
|
|
|
|
"cos(pi)", // 180 degrees
|
|
|
|
|
"-1",
|
|
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
//
|
|
|
|
|
// functions of symbols
|
|
|
|
|
//
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
|
|
"log(a)",
|
|
|
|
|
"log(a)",
|
|
|
|
|
|
|
|
|
|
"exp(a)",
|
|
|
|
|
"exp(a)",
|
|
|
|
|
|
|
|
|
|
"cos(a)",
|
|
|
|
|
"cos(a)",
|
|
|
|
|
|
|
|
|
|
"sin(a)",
|
|
|
|
|
"sin(a)",
|
|
|
|
|
|
|
|
|
|
"tan(a)",
|
|
|
|
|
"tan(a)",
|
|
|
|
|
|
|
|
|
|
"arccos(a)",
|
|
|
|
|
"arccos(a)",
|
|
|
|
|
|
|
|
|
|
"arcsin(a)",
|
|
|
|
|
"arcsin(a)",
|
|
|
|
|
|
|
|
|
|
"arctan(a)",
|
|
|
|
|
"arctan(a)",
|
|
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
//
|
|
|
|
|
// functions of floating point
|
|
|
|
|
//
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
|
|
"log(2.0)",
|
|
|
|
|
"0.693147",
|
|
|
|
|
|
|
|
|
|
"exp(2.0)",
|
|
|
|
|
"7.38906",
|
|
|
|
|
|
|
|
|
|
"cos(1.2)",
|
|
|
|
|
"0.362358",
|
|
|
|
|
|
|
|
|
|
"sin(1.2)",
|
|
|
|
|
"0.932039",
|
|
|
|
|
|
|
|
|
|
"tan(1.2)",
|
|
|
|
|
"2.57215",
|
|
|
|
|
|
|
|
|
|
"arccos(.12)",
|
|
|
|
|
"1.45051",
|
|
|
|
|
|
|
|
|
|
"arcsin(.12)",
|
|
|
|
|
"0.12029",
|
|
|
|
|
|
|
|
|
|
"arctan(.12)",
|
|
|
|
|
"0.119429",
|
|
|
|
|
|
|
|
|
|
"sqrt(-2.0)",
|
|
|
|
|
"1.41421*i",
|
|
|
|
|
|
|
|
|
|
/* powers of negative numbers */
|
|
|
|
|
|
|
|
|
|
#if 0
|
|
|
|
|
"(-1)^(2/3)",
|
|
|
|
|
"1",
|
|
|
|
|
|
|
|
|
|
"(-1)^(-2/3)",
|
|
|
|
|
"1",
|
|
|
|
|
|
|
|
|
|
"(-2)^(1/2)",
|
|
|
|
|
"i*2^(1/2)",
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
// complex numbers
|
|
|
|
|
|
|
|
|
|
"i",
|
|
|
|
|
"i",
|
|
|
|
|
|
|
|
|
|
"i^2",
|
|
|
|
|
"-1",
|
|
|
|
|
|
|
|
|
|
"1/i",
|
|
|
|
|
"-i",
|
|
|
|
|
|
|
|
|
|
"(1/i)^2",
|
|
|
|
|
"-1",
|
|
|
|
|
|
|
|
|
|
"(-1)^(1/2)",
|
|
|
|
|
"i",
|
|
|
|
|
|
|
|
|
|
"conj(x+i*y)",
|
|
|
|
|
"x-i*y",
|
|
|
|
|
|
|
|
|
|
"conj((-1)^(1/3))",
|
|
|
|
|
"-(-1)^(2/3)",
|
|
|
|
|
|
|
|
|
|
"conj((-1)^(2/3))",
|
|
|
|
|
"-(-1)^(1/3)",
|
|
|
|
|
|
|
|
|
|
"conj((-1)^(1/10))",
|
|
|
|
|
"-(-1)^(9/10)",
|
|
|
|
|
|
|
|
|
|
"conj((-1)^(4/3))",
|
|
|
|
|
"(-1)^(2/3)",
|
|
|
|
|
|
|
|
|
|
"conj((-1)^(7/3))",
|
|
|
|
|
"-(-1)^(2/3)",
|
|
|
|
|
|
|
|
|
|
"(3+2*i)*(1+4*i)",
|
|
|
|
|
"-5+14*i",
|
|
|
|
|
#if 0
|
|
|
|
|
"(-1)^(1/3)",
|
|
|
|
|
"1/2+1/2*i*3^(1/2)",
|
|
|
|
|
|
|
|
|
|
"a=i^(1/3)",
|
|
|
|
|
"a",
|
|
|
|
|
|
|
|
|
|
"a*a*a",
|
|
|
|
|
"i",
|
|
|
|
|
|
|
|
|
|
"a=(1/3*i)^(1/3)",
|
|
|
|
|
"a",
|
|
|
|
|
|
|
|
|
|
"a*a*a",
|
|
|
|
|
"1/3*i",
|
|
|
|
|
|
|
|
|
|
"a=(-1/3*i)^(1/3)",
|
|
|
|
|
"a",
|
|
|
|
|
|
|
|
|
|
"a*a*a",
|
|
|
|
|
"-1/3*i",
|
|
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#if 0
|
|
|
|
|
|
|
|
|
|
"A=4*(a+b)",
|
|
|
|
|
"A",
|
|
|
|
|
|
|
|
|
|
"B=-3*(a+b)",
|
|
|
|
|
"B",
|
|
|
|
|
|
|
|
|
|
"C=2*(a+b)",
|
|
|
|
|
"C",
|
|
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
#if 0
|
|
|
|
|
|
|
|
|
|
"A+B+C",
|
|
|
|
|
"3*(a+b)",
|
|
|
|
|
|
|
|
|
|
"A+C+B",
|
|
|
|
|
"3*(a+b)",
|
|
|
|
|
|
|
|
|
|
"B+A+C",
|
|
|
|
|
"3*(a+b)",
|
|
|
|
|
|
|
|
|
|
"B+C+A",
|
|
|
|
|
"3*(a+b)",
|
|
|
|
|
|
|
|
|
|
"C+A+B",
|
|
|
|
|
"3*(a+b)",
|
|
|
|
|
|
|
|
|
|
"C+B+A",
|
|
|
|
|
"3*(a+b)",
|
|
|
|
|
#endif
|
|
|
|
|
"A=quote(A)",
|
|
|
|
|
"A",
|
|
|
|
|
|
|
|
|
|
"B=quote(B)",
|
|
|
|
|
"B",
|
|
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
//
|
|
|
|
|
// integral
|
|
|
|
|
//
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
|
|
"integral(a,x)",
|
|
|
|
|
"a*x",
|
|
|
|
|
|
|
|
|
|
"integral(a*b,x)",
|
|
|
|
|
"a*b*x",
|
|
|
|
|
|
|
|
|
|
"integral(x,x)",
|
|
|
|
|
"1/2*x^2",
|
|
|
|
|
|
|
|
|
|
"integral(a*x,x)",
|
|
|
|
|
"1/2*a*x^2",
|
|
|
|
|
|
|
|
|
|
"integral(a*b*x,x)",
|
|
|
|
|
"1/2*a*b*x^2",
|
|
|
|
|
|
|
|
|
|
"integral(a+b,x)",
|
|
|
|
|
"a*x+b*x",
|
|
|
|
|
|
|
|
|
|
"integral(1/x,x)",
|
|
|
|
|
"log(x)",
|
|
|
|
|
|
|
|
|
|
"integral(x^a,x)",
|
|
|
|
|
"x^(1+a)/(1+a)",
|
|
|
|
|
|
|
|
|
|
"integral(exp(x),x)",
|
|
|
|
|
"exp(x)",
|
|
|
|
|
|
|
|
|
|
"integral(exp(a*x),x)",
|
|
|
|
|
"exp(a*x)/a",
|
|
|
|
|
|
|
|
|
|
"integral(exp(a*x+b),x)",
|
|
|
|
|
"exp(b+a*x)/a",
|
|
|
|
|
|
|
|
|
|
"integral(x*exp(A*x^2+B),x)",
|
|
|
|
|
"exp(B+A*x^2)/(2*A)",
|
|
|
|
|
|
|
|
|
|
"integral(log(x),x)",
|
|
|
|
|
"-x+x*log(x)",
|
|
|
|
|
|
|
|
|
|
"integral(log(a*x+b),x)",
|
|
|
|
|
"-x+x*log(b+a*x)+b*log(b+a*x)/a",
|
|
|
|
|
|
|
|
|
|
"integral(sin(x),x)",
|
|
|
|
|
"-cos(x)",
|
|
|
|
|
|
|
|
|
|
"integral(cos(x),x)",
|
|
|
|
|
"sin(x)",
|
|
|
|
|
|
|
|
|
|
"integral(sin(x)*cos(x),x)", // 318
|
|
|
|
|
"1/2*sin(x)^2",
|
|
|
|
|
|
|
|
|
|
"integral(sin(a*x)*cos(a*x),x)", // 318
|
|
|
|
|
"sin(a*x)^2/(2*a)",
|
|
|
|
|
|
|
|
|
|
// integral w/o 2nd arg
|
|
|
|
|
|
|
|
|
|
"integral(1+x+x^2+x^3)",
|
|
|
|
|
"x+1/2*x^2+1/3*x^3+1/4*x^4",
|
|
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
//
|
|
|
|
|
// dsolve
|
|
|
|
|
//
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
|
|
// "dsolve(d(y(x),x)-2*x*y(x)-x,y(x),x)",
|
|
|
|
|
// "-1/2+C*exp(x^2)",
|
|
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
//
|
|
|
|
|
// sum of tensors
|
|
|
|
|
//
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
|
|
"((a,b),(c,d))+((1,2),(3,4))",
|
|
|
|
|
"((1+a,2+b),(3+c,4+d))",
|
|
|
|
|
|
|
|
|
|
// mixed rank
|
|
|
|
|
|
|
|
|
|
"(b1,b2,b3)+((a11,a12,a13),(a21,a22,a23),(a31,a32,a33))",
|
|
|
|
|
"(b1,b2,b3)+((a11,a12,a13),(a21,a22,a23),(a31,a32,a33))",
|
|
|
|
|
|
|
|
|
|
//----------------------------------------------------------------------------
|
|
|
|
|
//
|
|
|
|
|
// scalar times tensor
|
|
|
|
|
//
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
|
|
"c=((1,1),(1,1))",
|
|
|
|
|
"((1,1),(1,1))",
|
|
|
|
|
|
|
|
|
|
"a*b*c",
|
|
|
|
|
"((a*b,a*b),(a*b,a*b))",
|
|
|
|
|
|
|
|
|
|
"c*d*e",
|
|
|
|
|
"((d*e,d*e),(d*e,d*e))",
|
|
|
|
|
|
|
|
|
|
"a*b*c*d*e",
|
|
|
|
|
"((a*b*d*e,a*b*d*e),(a*b*d*e,a*b*d*e))",
|
|
|
|
|
|
|
|
|
|
"c=quote(c)",
|
|
|
|
|
"c",
|
|
|
|
|
|
|
|
|
|
// det
|
|
|
|
|
|
|
|
|
|
"det(a)",
|
|
|
|
|
"det(a)",
|
|
|
|
|
|
|
|
|
|
"det(((1,2),(3,4)))",
|
|
|
|
|
"-2",
|
|
|
|
|
|
|
|
|
|
"det(((2,3,-2,5),(6,-2,1,4),(5,10,3,-2),(-1,2,2,3)))",
|
|
|
|
|
"-1629",
|
|
|
|
|
|
|
|
|
|
"det(A)",
|
|
|
|
|
"det(A)",
|
|
|
|
|
|
|
|
|
|
"det(((A/(A-B),1),(B/(A-B),1)))",
|
|
|
|
|
"A/(A-B)-B/(A-B)", // add "simplify" to get 1
|
|
|
|
|
|
|
|
|
|
// make sure the sign of det is handled for row interchange
|
|
|
|
|
|
|
|
|
|
"det(((1,0,0),(0,0,1),(0,1,0)))",
|
|
|
|
|
"-1",
|
|
|
|
|
|
|
|
|
|
"det(((a11-x,a12),(a21,a22-x)))-(a11*a22-a11*x-a12*a21-a22*x+x^2)",
|
|
|
|
|
"0",
|
|
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
//
|
|
|
|
|
// adj
|
|
|
|
|
//
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
|
|
"adj(a)",
|
|
|
|
|
"adj(a)",
|
|
|
|
|
|
|
|
|
|
"adj(((1,2),(3,4)))",
|
|
|
|
|
"((4,-2),(-3,1))",
|
|
|
|
|
|
|
|
|
|
"adj(((2,3,-2,5),(6,-2,1,4),(5,10,3,-2),(-1,2,2,3)))",
|
|
|
|
|
"((-4,-177,-73,194),(-117,117,-99,-27),(310,-129,-44,-374),(-130,-51,71,-211))",
|
|
|
|
|
|
|
|
|
|
"adj(A)",
|
|
|
|
|
"adj(A)",
|
|
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
//
|
|
|
|
|
// inv
|
|
|
|
|
//
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
|
|
"inv(a)",
|
|
|
|
|
"inv(a)",
|
|
|
|
|
|
|
|
|
|
"invg(a)",
|
|
|
|
|
"invg(a)",
|
|
|
|
|
|
|
|
|
|
"inv(((1,2),(3,4)))",
|
|
|
|
|
"((-2,1),(3/2,-1/2))",
|
|
|
|
|
|
|
|
|
|
"inner(((1,2),(3,4)),inv(((1,2),(3,4))))",
|
|
|
|
|
"((1,0),(0,1))",
|
|
|
|
|
|
|
|
|
|
"inv(hilbert(3))",
|
|
|
|
|
"((9,-36,30),(-36,192,-180),(30,-180,180))",
|
|
|
|
|
|
|
|
|
|
"invg(hilbert(3))",
|
|
|
|
|
"((9,-36,30),(-36,192,-180),(30,-180,180))",
|
|
|
|
|
|
|
|
|
|
"inv(((a,a),(a,a)))",
|
|
|
|
|
"Stop: inverse of singular matrix",
|
|
|
|
|
|
|
|
|
|
// power of tensor
|
|
|
|
|
|
|
|
|
|
"A=((1,2),(3,4))",
|
|
|
|
|
"((1,2),(3,4))",
|
|
|
|
|
|
|
|
|
|
"inner(A,1/A)",
|
|
|
|
|
"((1,0),(0,1))",
|
|
|
|
|
|
|
|
|
|
"inner(A,A^(-1))",
|
|
|
|
|
"((1,0),(0,1))",
|
|
|
|
|
|
|
|
|
|
"inner(A,A)-A^2",
|
|
|
|
|
"((0,0),(0,0))",
|
|
|
|
|
|
|
|
|
|
"A=quote(A)",
|
|
|
|
|
"",
|
|
|
|
|
|
|
|
|
|
// rank
|
|
|
|
|
|
|
|
|
|
"rank(A)",
|
|
|
|
|
"0",
|
|
|
|
|
|
|
|
|
|
"rank(1)",
|
|
|
|
|
"0",
|
|
|
|
|
|
|
|
|
|
"rank((a,b))",
|
|
|
|
|
"1",
|
|
|
|
|
|
|
|
|
|
"rank(((a,b),(c,d)))",
|
|
|
|
|
"2",
|
|
|
|
|
|
|
|
|
|
// setup for vector identities
|
|
|
|
|
|
|
|
|
|
"cross(u,v) = ("
|
|
|
|
|
" u[2] v[3] - u[3] v[2],"
|
|
|
|
|
" u[3] v[1] - u[1] v[3],"
|
|
|
|
|
" u[1] v[2] - u[2] v[1])",
|
|
|
|
|
"",
|
|
|
|
|
|
|
|
|
|
"div(v) = contract(d(v,(x,y,z)),1,2)",
|
|
|
|
|
"",
|
|
|
|
|
|
|
|
|
|
"grad(v) = d(v,(x,y,z))",
|
|
|
|
|
"",
|
|
|
|
|
|
|
|
|
|
"curl(f) = ("
|
|
|
|
|
" d(f[3],y) - d(f[2],z),"
|
|
|
|
|
" d(f[1],z) - d(f[3],x),"
|
|
|
|
|
" d(f[2],x) - d(f[1],y))",
|
|
|
|
|
"",
|
|
|
|
|
|
|
|
|
|
"laplacian(f) = d(d(f,x),x) + d(d(f,y),y) + d(d(f,z),z)",
|
|
|
|
|
"",
|
|
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
//
|
|
|
|
|
// gradient
|
|
|
|
|
//
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
|
|
"d(f(x),x)",
|
|
|
|
|
"d(f(x),x)",
|
|
|
|
|
|
|
|
|
|
"d(f(x,y,z),(x,y,z))",
|
|
|
|
|
"(d(f(x,y,z),x),d(f(x,y,z),y),d(f(x,y,z),z))",
|
|
|
|
|
|
|
|
|
|
"d((f(x),g(x)),x)",
|
|
|
|
|
"(d(f(x),x),d(g(x),x))",
|
|
|
|
|
|
|
|
|
|
"grad(V())",
|
|
|
|
|
"(d(V(),x),d(V(),y),d(V(),z))",
|
|
|
|
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
//
|
|
|
|
|
// curl
|
|
|
|
|
//
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
|
|
|
|
|
|
|
|
"curl((X(),Y(),Z()),(x,y,z))",
|
|
|
|
|
"(-d(Y(),z)+d(Z(),y),d(X(),z)-d(Z(),x),-d(X(),y)+d(Y(),x))",
|
|
|
|
|
|
|
|
|
|
"curl((X(),Y(),Z()))",
|
|
|
|
|
"(-d(Y(),z)+d(Z(),y),d(X(),z)-d(Z(),x),-d(X(),y)+d(Y(),x))",
|
|
|
|
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//-----------------------------------------------------------------------------
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//
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// vector identities from AMA205
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//
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//-----------------------------------------------------------------------------
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"F=(FX(),FY(),FZ())",
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"F",
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"G=(GX(),GY(),GZ())",
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"G",
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"f=f()",
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"f",
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"g=g()",
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"g",
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"div(curl(F))",
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"0",
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"curl(grad(f))",
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"(0,0,0)",
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"div(grad(f))-laplacian(f)",
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"0",
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"curl(curl(F))-grad(div(F))+laplacian(F)",
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"(0,0,0)",
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"grad(f*g)-f*grad(g)-g*grad(f)",
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"(0,0,0)",
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"div(f*F)-f*div(F)-inner(grad(f),F)",
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"0",
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"curl(f*F)-f*curl(F)-cross(grad(f),F)",
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"(0,0,0)",
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"grad(inner(F,G))-inner(G,grad(F))-inner(F,grad(G))",
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"(0,0,0)",
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"grad(inner(F,G))-inner(grad(F),G)-inner(grad(G),F)-cross(G,curl(F))-cross(F,curl(G))",
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"(0,0,0)",
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"div(cross(F,G))-inner(G,curl(F))+inner(F,curl(G))",
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"0",
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"curl(cross(F,G))-F*div(G)+G*div(F)-inner(grad(F),G)+inner(grad(G),F)",
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"(0,0,0)",
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// hilbert
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"det(hilbert(6))",
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"1/186313420339200000",
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// normalize angle
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"(-1)^(8/3)",
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"(-1)^(2/3)",
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"(-1)^(7/3)",
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"(-1)^(1/3)",
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"(-1)^(5/3)",
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"-(-1)^(2/3)",
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"(-1)^(4/3)",
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"-(-1)^(1/3)",
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"(-1)^(2/3)",
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"(-1)^(2/3)",
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"(-1)^(1/3)",
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"(-1)^(1/3)",
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"(-1)^(-1/3)",
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"-(-1)^(2/3)",
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"(-1)^(-2/3)",
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"-(-1)^(1/3)",
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"(-1)^(-4/3)",
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"(-1)^(2/3)",
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"(-1)^(-5/3)",
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"(-1)^(1/3)",
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"(-1)^(-7/3)",
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"-(-1)^(2/3)",
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"(-1)^(-8/3)",
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"-(-1)^(1/3)",
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// power() can return a multiply, make sure multiply() handles it
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// "-1/2*i*(-exp(-i*pi/6)+exp(i*pi/6))",
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// "1/2*(-1)^(1/3)-1/2*(-1)^(2/3)",
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// from the jargon file
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"1000!",
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"40238726007709377354370243392300398571937486421071"
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"46325437999104299385123986290205920442084869694048"
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"00479988610197196058631666872994808558901323829669"
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"94459099742450408707375991882362772718873251977950"
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"59509952761208749754624970436014182780946464962910"
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"56393887437886487337119181045825783647849977012476"
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"63288983595573543251318532395846307555740911426241"
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"74743493475534286465766116677973966688202912073791"
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"43853719588249808126867838374559731746136085379534"
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"52422158659320192809087829730843139284440328123155"
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"86110369768013573042161687476096758713483120254785"
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"89320767169132448426236131412508780208000261683151"
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"02734182797770478463586817016436502415369139828126"
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"48102130927612448963599287051149649754199093422215"
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"66832572080821333186116811553615836546984046708975"
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"60290095053761647584772842188967964624494516076535"
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"34081989013854424879849599533191017233555566021394"
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"50399736280750137837615307127761926849034352625200"
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"01588853514733161170210396817592151090778801939317"
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"81141945452572238655414610628921879602238389714760"
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"88506276862967146674697562911234082439208160153780"
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"88989396451826324367161676217916890977991190375403"
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"12746222899880051954444142820121873617459926429565"
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"81746628302955570299024324153181617210465832036786"
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"90611726015878352075151628422554026517048330422614"
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"39742869330616908979684825901254583271682264580665"
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"26769958652682272807075781391858178889652208164348"
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"34482599326604336766017699961283186078838615027946"
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"59551311565520360939881806121385586003014356945272"
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"24206344631797460594682573103790084024432438465657"
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"24501440282188525247093519062092902313649327349756"
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"55139587205596542287497740114133469627154228458623"
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"77387538230483865688976461927383814900140767310446"
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"64025989949022222176590433990188601856652648506179"
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"97023561938970178600408118897299183110211712298459"
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"01641921068884387121855646124960798722908519296819"
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"37238864261483965738229112312502418664935314397013"
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"74285319266498753372189406942814341185201580141233"
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"44828015051399694290153483077644569099073152433278"
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"28826986460278986432113908350621709500259738986355"
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"42771967428222487575867657523442202075736305694988"
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"25087968928162753848863396909959826280956121450994"
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"87170124451646126037902930912088908694202851064018"
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"21543994571568059418727489980942547421735824010636"
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"77404595741785160829230135358081840096996372524230"
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"56085590370062427124341690900415369010593398383577"
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"79394109700277534720000000000000000000000000000000"
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"00000000000000000000000000000000000000000000000000"
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"00000000000000000000000000000000000000000000000000"
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"00000000000000000000000000000000000000000000000000"
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"00000000000000000000000000000000000000000000000000"
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"000000000000000000",
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// float
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"float(2/3)",
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"0.666667",
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"float(hilbert(3))",
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"((1,0.5,0.333333),(0.5,0.333333,0.25),(0.333333,0.25,0.2))",
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"a=pi",
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"a",
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"float(a)",
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"3.14159",
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"a=exp(1)",
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"a",
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"float(a)",
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"2.71828",
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"a=quote(a)",
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"a",
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// test self-referencing arg
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"f(x)=eval(x)+1",
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"",
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"f(x+1)",
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"2+x",
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// test indexed formal arg
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"f(x)=do(x[1]=3,x)",
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"",
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"x=(a,b)",
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"",
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"f(x)",
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"(3,b)",
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"x",
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"(a,b)",
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"f=quote(f)",
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"",
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"x=quote(x)",
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"",
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// last
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"a=2+3",
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"",
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"last",
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"5",
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"a=quote(a)",
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"",
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// equality of tensors
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"testeq((1,2),(1,2))",
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2005-09-02 21:41:19 +02:00
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"true",
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2005-08-07 16:42:42 +02:00
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"testeq((1,2),(1,3))",
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2005-09-02 21:41:19 +02:00
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"false",
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2005-08-07 16:42:42 +02:00
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// the "check" function with tensor arg
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"check((1,2)-(1,2))",
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"",
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// nil
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"nil",
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"nil",
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};
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void
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test_all(void)
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{
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test(__FILE__, script, sizeof(script) / sizeof (char *));
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}
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extern char out_buf[];
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extern int out_count;
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void
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test(char *file, char **s, int n)
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{
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int i;
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char *t;
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test_flag = 1;
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for (i = 0; i < n; i++) {
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logout(s[i]);
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logout("\n");
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if (s[i][0] == '#')
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continue;
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out_count = 0;
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run(s[i]);
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t = s[i];
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while (*t && *t != '=')
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t++;
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if (*t == '=') {
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i++;
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continue;
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}
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out_buf[out_count] = 0;
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t = out_buf;
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// skip leading newlines
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while (*t == '\n')
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t++;
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// remove trailing newlines
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while (out_count && out_buf[out_count - 1] == '\n')
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out_buf[--out_count] = 0;
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i++;
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if (strcmp(t, s[i]) == 0)
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continue;
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// make copy because logout clobbers out_buf
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t = strdup(t);
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logout("expected to get the following result:\n");
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logout(s[i]);
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logout("\n");
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logout("got this result instead:\n");
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logout(t);
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logout("\n");
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logout(file);
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logout("\n");
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free(t);
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errout();
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}
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test_flag = 0;
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}
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