862 lines
12 KiB
C
862 lines
12 KiB
C
#if SELFTEST
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static char *s[] = {
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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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"",
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"b=quote(b)",
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"",
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"c=quote(c)",
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"",
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"d=quote(d)",
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"",
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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)",
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"a+b",
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"(a+b)+0",
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"a+b",
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"1+2",
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"3",
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"a+0",
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"a",
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"0+a",
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"a",
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"a+a",
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"2*a",
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"a+2*a",
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"3*a",
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"2*a+a",
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"3*a",
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"2*a+3*a",
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"5*a",
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"a*b+a*b",
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"2*a*b",
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"a*b+2*a*b",
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"3*a*b",
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"2*a*b+a*b",
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"3*a*b",
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"2*a*b+3*a*b",
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"5*a*b",
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"1/2*a+1/2*a",
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"a",
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"1/2*a*b+1/2*a*b",
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"a*b",
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"a+a+a",
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"3*a",
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"a+b+b",
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"a+2*b",
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"2*a+2*a",
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"4*a",
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"1/4*a-1/4*a",
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"0",
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"(a+b+c+d)-(a+b+c+d)",
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"0",
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/* power */
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"0^0", // see ross' book, p. 129
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"1",
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"a^0",
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"1",
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"a^1",
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"a",
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"1^a",
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"1",
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"a^a",
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"a^a",
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"2^(1/2)",
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"2^(1/2)",
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// "a^(b+c)",
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// "a^b*a^c",
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// "a^(b+c+d)",
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// "a^b*a^c*a^d",
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"(a*b)^c",
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"a^c*b^c",
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"(a*b*c)^d",
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"a^d*b^d*c^d",
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"2^3",
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"8",
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"a^(2*a)",
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"a^(2*a)",
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"a^(2*a*b)",
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"a^(2*a*b)",
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"(a^2)^3",
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"a^6",
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"a^2^3",
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"a^8",
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/*
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"12^(1/2)",
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"2*3^(1/2)",
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"12^(-1/2)",
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"1/2*(1/3)^(1/2)",
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"8^(2/3)",
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"4",
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"8^(-2/3)",
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"1/4",
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"2^(3/2)",
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"2*2^(1/2)",
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"(3/2)^(-1/2)",
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"(2/3)^(1/2)",
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"(3/4)^(1/2)",
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"1/2*3^(1/2)",
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"(9/4)^(1/2)",
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"3/2",
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"(9/4)^(3/2)",
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"27/8",
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"3*3^(-1/2)",
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"3^(1/2)",
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*/
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"(a^b)^c",
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"a^(b*c)",
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"((a+b)^(-2))^(-1)",
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// "a^2+b^2+2*a*b",
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"2*a*b+a^2+b^2",
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#if 0
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"(-27)^(1/3)",
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"-3",
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#endif
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// make sure scanner doesn't produce imaginary
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// "quote((-a/b)^(1/2))",
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// "(-a/b)^(1/2)",
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#if 0
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/* roots of large numbers */
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"x=10^20",
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"x",
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"x^(1/2)",
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"10000000000",
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"x^(-1/2)",
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"1/10000000000",
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#endif
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// functions of symbols
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"log(a)",
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"log(a)",
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"exp(a)",
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"exp(a)",
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"cos(a)",
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"cos(a)",
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"sin(a)",
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"sin(a)",
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"tan(a)",
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"tan(a)",
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"arccos(a)",
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"arccos(a)",
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"arcsin(a)",
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"arcsin(a)",
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"arctan(a)",
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"arctan(a)",
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// functions of floating point
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"log(2.0)",
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"0.693147",
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"exp(2.0)",
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"7.38906",
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"cos(1.2)",
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"0.362358",
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"sin(1.2)",
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"0.932039",
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"tan(1.2)",
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"2.57215",
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"arccos(.12)",
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"1.45051",
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"arcsin(.12)",
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"0.12029",
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"arctan(.12)",
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"0.119429",
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"sqrt(-2.0)",
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"1.41421*i",
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// complex numbers
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"i",
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"(-1)^(1/2)",
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"i^2",
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"-1",
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"1/i",
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"-i",
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"(1/i)^2",
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"-1",
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"(-1)^(1/2)",
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"i",
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"conj(x+i*y)",
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"x-i*y",
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"conj((-1)^(1/3))",
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"-(-1)^(2/3)",
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"conj((-1)^(2/3))",
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"-(-1)^(1/3)",
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"conj((-1)^(1/10))",
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"-(-1)^(9/10)",
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"conj((-1)^(4/3))",
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"(-1)^(2/3)",
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"conj((-1)^(7/3))",
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"-(-1)^(2/3)",
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"(3+2*i)*(1+4*i)",
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"-5+14*i",
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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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// integral
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"integral(a,x)-a*x",
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"0",
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"integral(a*b,x)-a*b*x",
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"0",
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"integral(x,x)-1/2*x^2",
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"0",
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"integral(a*x,x)-1/2*a*x^2",
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"0",
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"integral(a*b*x,x)",
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"1/2*a*b*x^2",
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"integral(a+b,x)-a*x-b*x",
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"0",
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"integral(1/x,x)",
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"log(x)",
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"integral(x^a,x)",
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"x^(1+a)/(1+a)",
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"integral(exp(x),x)",
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"exp(x)",
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"integral(exp(a*x),x)",
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"exp(a*x)/a",
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"integral(exp(a*x+b),x)-exp(b+a*x)/a",
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"0",
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"integral(x*exp(A*x^2+B),x)-exp(B+A*x^2)/(2*A)",
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"0",
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"integral(log(x),x)+x-x*log(x)",
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"0",
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"integral(log(a*x+b),x)+x-x*log(b+a*x)-b*log(b+a*x)/a",
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"0",
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"integral(sin(x),x)",
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"-cos(x)",
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"integral(cos(x),x)",
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"sin(x)",
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"integral(sin(x)*cos(x),x)", // 318
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"1/2*sin(x)^2",
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"integral(sin(a*x)*cos(a*x),x)", // 318
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"sin(a*x)^2/(2*a)",
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// integral w/o 2nd arg
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"integral(1+x+x^2+x^3)-(x+1/2*x^2+1/3*x^3+1/4*x^4)",
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"0",
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//-----------------------------------------------------------------------------
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//
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// dsolve
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//
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//-----------------------------------------------------------------------------
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// "dsolve(d(y(x),x)-2*x*y(x)-x,y(x),x)",
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// "-1/2+C*exp(x^2)",
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//-----------------------------------------------------------------------------
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//
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// sum of tensors
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//
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//-----------------------------------------------------------------------------
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"((a,b),(c,d))+((1,2),(3,4))",
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"((1+a,2+b),(3+c,4+d))",
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// mixed rank
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"(b1,b2,b3)+((a11,a12,a13),(a21,a22,a23),(a31,a32,a33))",
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"(b1,b2,b3)+((a11,a12,a13),(a21,a22,a23),(a31,a32,a33))",
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//----------------------------------------------------------------------------
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//
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// scalar times tensor
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//
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//-----------------------------------------------------------------------------
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"c=((1,1),(1,1))",
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"",
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"a*b*c",
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"((a*b,a*b),(a*b,a*b))",
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"c*d*f",
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"((d*f,d*f),(d*f,d*f))",
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"a*b*c*d*f",
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"((a*b*d*f,a*b*d*f),(a*b*d*f,a*b*d*f))",
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"c=quote(c)",
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"",
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// det
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"det(a)",
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"det(a)",
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"det(((1,2),(3,4)))",
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"-2",
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"det(((2,3,-2,5),(6,-2,1,4),(5,10,3,-2),(-1,2,2,3)))",
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"-1629",
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"det(A)",
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"det(A)",
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"det(((A/(A-B),1),(B/(A-B),1)))",
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"A/(A-B)-B/(A-B)", // add "simplify" to get 1
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// make sure the sign of det is handled for row interchange
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"det(((1,0,0),(0,0,1),(0,1,0)))",
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"-1",
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"det(((a11-x,a12),(a21,a22-x)))-(a11*a22-a11*x-a12*a21-a22*x+x^2)",
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"0",
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//-----------------------------------------------------------------------------
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//
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// inv
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//
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//-----------------------------------------------------------------------------
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"inv(a)",
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"inv(a)",
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"invg(a)",
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"invg(a)",
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"inv(((1,2),(3,4)))",
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"((-2,1),(3/2,-1/2))",
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"inner(((1,2),(3,4)),inv(((1,2),(3,4))))",
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"((1,0),(0,1))",
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"inv(hilbert(3))",
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"((9,-36,30),(-36,192,-180),(30,-180,180))",
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"invg(hilbert(3))",
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"((9,-36,30),(-36,192,-180),(30,-180,180))",
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"inv(((a,a),(a,a)))",
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"Stop: inverse of singular matrix",
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// power of tensor
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"A=((1,2),(3,4))",
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"",
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"inner(A,1/A)",
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"((1,0),(0,1))",
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"inner(A,A^(-1))",
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"((1,0),(0,1))",
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"inner(A,A)-A^2",
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"((0,0),(0,0))",
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"A=quote(A)",
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"",
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// rank
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"rank(A)",
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"0",
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"rank(1)",
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"0",
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"rank((a,b))",
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"1",
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"rank(((a,b),(c,d)))",
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"2",
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// setup for vector identities
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"cross(u,v) = ("
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" u[2] v[3] - u[3] v[2],"
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" u[3] v[1] - u[1] v[3],"
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" u[1] v[2] - u[2] v[1])",
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"",
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"div(v) = contract(d(v,(x,y,z)),1,2)",
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"",
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"grad(v) = d(v,(x,y,z))",
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"",
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"curl(f) = ("
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" d(f[3],y) - d(f[2],z),"
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" d(f[1],z) - d(f[3],x),"
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" d(f[2],x) - d(f[1],y))",
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"",
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"laplacian(f) = d(d(f,x),x) + d(d(f,y),y) + d(d(f,z),z)",
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"",
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//-----------------------------------------------------------------------------
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//
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// gradient
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//
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//-----------------------------------------------------------------------------
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"d(f(x),x)",
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"d(f(x),x)",
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"d(f(x,y,z),(x,y,z))",
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"(d(f(x,y,z),x),d(f(x,y,z),y),d(f(x,y,z),z))",
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"d((f(x),g(x)),x)",
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"(d(f(x),x),d(g(x),x))",
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"grad(V())",
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"(d(V(),x),d(V(),y),d(V(),z))",
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//-----------------------------------------------------------------------------
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//
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// curl
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//
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//-----------------------------------------------------------------------------
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"curl((X(),Y(),Z()),(x,y,z))",
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"(-d(Y(),z)+d(Z(),y),d(X(),z)-d(Z(),x),-d(X(),y)+d(Y(),x))",
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"curl((X(),Y(),Z()))",
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"(-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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"",
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"G=(GX(),GY(),GZ())",
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"",
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"f=ff()",
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"",
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"g=gg()",
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"",
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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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"",
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"float(a)",
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"3.14159",
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"a=exp(1)",
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"",
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"float(a)",
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"2.71828",
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"a=quote(a)",
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"",
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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)-(2+x)",
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"0",
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// equality of tensors
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"testeq((1,2),(1,2))",
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"1",
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"testeq((1,2),(1,3))",
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"0",
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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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"",
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// ensure scanner does not discard 1.0
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"1.0 1/2",
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"0.5",
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"1/2 1.0",
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"0.5",
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// the variable 'last' should be the last thing displayed
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"123",
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"123",
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"AA=456",
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"",
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"last",
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"123",
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};
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#endif
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