From 39b4a2005fedf83d1c4e59a967b52e99bb9c6e4a Mon Sep 17 00:00:00 2001 From: George Weigt <gweigt@users.sourceforge.net> Date: Sat, 1 Nov 2008 11:22:01 -0700 Subject: [PATCH] *** empty log message *** --- help.html | 1385 +++++++++++++++++++++++++++-------------------------- 1 file changed, 708 insertions(+), 677 deletions(-) diff --git a/help.html b/help.html index d7ffa1d..542a896 100644 --- a/help.html +++ b/help.html @@ -1,677 +1,708 @@ -<html> -<head> -</head> -<body> -<tt> - -<p> -Click <a href="examples">here</a> for examples that can be pasted into Eigenmath's edit window. - -<p> -<img src="man.jpg"></td> - -<p> -<a href="Eigenmath.pdf">Download Eigenmath.pdf</a> - -<p> -<hr> - -<p> -<table cellspacing=20><tr><td valign="top"><tt> - -<a href="#abs">abs</a><br> -<a href="#adj">adj</a><br> -<a href="#and">and</a><br> -<a href="#arccos">arccos</a><br> -<a href="#arccosh">arccosh</a><br> -<a href="#arcsin">arcsin</a><br> -<a href="#arcsinh">arcsinh</a><br> -<a href="#arctan">arctan</a><br> -<a href="#arctanh">arctanh</a><br> -<a href="#arg">arg</a><br> -<a href="#ceiling">ceiling</a><br> -<a href="#check">check</a><br> -<a href="#choose">choose</a><br> - -</tt></td><td valign="top"><tt> - -<a href="#circexp">circexp</a><br> -<a href="#coeff">coeff</a><br> -<a href="#cofactor">cofactor</a><br> -<a href="#conj">conj</a><br> -<a href="#contract">contract</a><br> -<a href="#cos">cos</a><br> -<a href="#cosh">cosh</a><br> -<a href="#cross">cross</a><br> -<a href="#curl">curl</a><br> -<a href="#d">d</a><br> -<a href="#defint">defint</a><br> -<a href="#deg">deg</a><br> -<a href="#denominator">denominator</a><br> - -</tt></td><td valign="top"><tt> - -<a href="#det">det</a><br> -<a href="#dim">dim</a><br> -<a href="#do">do</a><br> -<a href="#dot">dot</a><br> -<a href="#draw">draw</a><br> -<a href="#erf">erf</a><br> -<a href="#erfc">erfc</a><br> -<a href="#eval">eval</a><br> -<a href="#exp">exp</a><br> -<a href="#expand">expand</a><img src="new.gif"><br> -<a href="#expcos">expcos</a><br> -<a href="#expsin">expsin</a><br> -<a href="#factor">factor</a><br> - -</tt></td><td valign="top"><tt> - -<a href="#factorial">factorial</a><br> -<a href="#filter">filter</a><br> -<a href="#float">float</a><br> -<a href="#floor">floor</a><br> -<a href="#for">for</a><br> -<a href="#gcd">gcd</a><br> -<a href="#hermite">hermite</a><br> -<a href="#hilbert">hilbert</a><br> -<a href="#imag">imag</a><br> -<a href="#inner">inner</a><br> -<a href="#integral">integral</a><br> -<a href="#inv">inv</a><br> -<a href="#isprime">isprime</a><br> - -</tt></td><td valign="top"><tt> - -<a href="#laguerre">laguerre</a><br> -<a href="#lcm">lcm</a><br> -<a href="#leading">leading</a><img src="new.gif"><br> -<a href="#legendre">legendre</a><br> -<a href="#log">log</a><br> -<a href="#mag">mag</a><br> -<a href="#mod">mod</a><br> -<a href="#not">not</a><br> -<a href="#nroots">nroots</a><br> -<a href="#numerator">numerator</a><br> -<a href="#or">or</a><br> -<a href="#outer">outer</a><br> -<a href="#polar">polar</a><br> - -</tt></td><td valign="top"><tt> - -<a href="#prime">prime</a><br> -<a href="#print">print</a><br> -<a href="#product">product</a><br> -<a href="#quote">quote</a><br> -<a href="#quotient">quotient</a><br> -<a href="#rank">rank</a><br> -<a href="#rationalize">rationalize</a><br> -<a href="#real">real</a><br> -<a href="#rect">rect</a><br> -<a href="#roots">roots</a><br> -<a href="#simplify">simplify</a><br> -<a href="#sin">sin</a><br> -<a href="#sinh">sinh</a><br> - -</tt></td><td valign="top"><tt> - -<a href="#sqrt">sqrt</a><br> -<a href="#stop">stop</a><br> -<a href="#subst">subst</a><br> -<a href="#sum">sum</a><br> -<a href="#tan">tan</a><br> -<a href="#tanh">tanh</a><br> -<a href="#taylor">taylor</a><br> -<a href="#test">test</a><br> -<a href="#transpose">transpose</a><br> -<a href="#unit">unit</a><br> -<a href="#zero">zero</a><br> - -</tt></td></tr></table> - -<p> -<hr> - -<p> -<h1><tt><a name="abs">abs(<i>x</i>)</a></tt></h1> -Returns the absolute value or vector length of x. -<a href="src/abs.cpp.html">src</a> - -<p> -<h1><tt><a name="adj">adj(<i>m</i>)</a></tt></h1> -Returns the adjunct of matrix m. -The inverse of m is equal to adj(m) divided by det(m). -<a href="src/adj.cpp.html">src</a> - -<p><h1><tt><a name="and">and(<i>a,b,...</i>)</a></tt></h1> -Logical-and of predicate expressions. -<a href="src/test.cpp.html#eval_and">src</a> - -<p> -<h1><tt><a name="arccos">arccos(<i>x</i>)</a></tt></h1> -Returns the inverse cosine of x. -<a href="src/arccos.cpp.html">src</a> - -<p> -<h1><tt><a name="arccosh">arccosh(<i>x</i>)</a></tt></h1> -Returns the inverse hyperbolic cosine of x. -<a href="src/arccosh.cpp.html">src</a> - -<p> -<h1><tt><a name="arcsin">arcsin(<i>x</i>)</a></tt></h1> -Returns the inverse sine of x. -<a href="src/arcsin.cpp.html">src</a> - -<p> -<h1><tt><a name="arcsinh">arcsinh(<i>x</i>)</a></tt></h1> -Returns the inverse hyperbolic sine of x. -<a href="src/arcsinh.cpp.html">src</a> - -<p> -<h1><tt><a name="arctan">arctan(<i>x</i>)</a></tt></h1> -Returns the inverse tangent of x. -<a href="src/arctan.cpp.html">src</a> - -<p> -<h1><tt><a name="arctanh">arctanh(<i>x</i>)</a></tt></h1> -Returns the inverse hyperbolic tangent of x. -<a href="src/arctanh.cpp.html">src</a> - -<p> -<h1><tt><a name="arg">arg(<i>z</i>)</a></tt></h1> -Returns the angle of complex z. -<a href="src/arg.cpp.html">src</a> - -<p> -<h1><tt><a name="ceiling">ceiling(<i>x</i>)</a></tt></h1> -Returns the smallest integer not less than x. -<a href="src/ceiling.cpp.html">src</a> - -<p> -<h1><tt><a name="check">check(<i>x</i>)</a></tt></h1> -If x is true then continue, else stop. -<a href="src/eval.cpp.html#eval_check">src </a> - -<p> -<h1><tt><a name="choose">choose(<i>n,k</i>)</a></tt></h1> -Returns the number of combinations of n items taken k at a time. -<a href="src/choose.cpp.html">src</a> - -<p> -<h1><tt><a name="circexp">circexp(<i>x</i>)</a></tt></h1> -Returns expression x with circular and hyperbolic functions converted to exponential forms. -Sometimes this will simplify an expression. -<a href="src/circexp.cpp.html">src</a> - -<p> -<h1><tt><a name="coeff">coeff(<i>p,x,n</i>)</a></tt></h1> -Returns the coefficient of x to the n in polynomial p. -The x argument can be omitted for polynomials in x. -<a href="src/coeff.cpp.html">src</a> - -<p> -<h1><tt><a name="cofactor">cofactor(<i>m,i,j</i>)</a></tt></h1> -Returns the cofactor of m for row i and column j. -<a href="src/cofactor.cpp.html">src</a> - -<p> -<h1><tt><a name="conj">conj(<i>z</i>)</a></tt></h1> -Returns the complex conjugate of z. -<a href="src/conj.cpp.html">src</a> - -<p> -<h1><tt><a name="contract">contract(<i>a,i,j</i>)</a></tt></h1> -Returns "a" summed over indices i and j. -If i and j are omitted then 1 and 2 are used. -contract(m) is equivalent to the trace of matrix m. -<a href="src/contract.cpp.html">src</a> - -<p> -<h1><tt><a name="cos">cos(<i>x</i>)</a></tt></h1> -Returns the cosine of x. -<a href="src/cos.cpp.html">src</a> - -<p> -<h1><tt><a name="cosh">cosh(<i>x</i>)</a></tt></h1> -Returns the hyperbolic cosine of x. -<a href="src/cosh.cpp.html">src</a> - -<p> -<h1><tt><a name="cross">cross(<i>u,v</i>)</a></tt></h1> -Returns the cross product of vectors u and v. - -<p> -<h1><tt><a name="curl">curl(<i>u</i>)</a></tt></h1> -Returns the curl of vector u. - -<p> -<h1><tt><a name="d">d(<i>f,x</i>)</a></tt></h1> -Returns the partial derivative of f with respect to x. -<a href="src/derivative.cpp.html">src</a> - -<p> -<h1><tt><a name="defint">defint(<i>f,x,a,b</i>)</a></tt></h1> -Returns the definite integral of f with respect to x -evaluated from "a" to b. -The argument list can be extended for multiple integrals. -For example, defint(f,x,a,b,y,c,d). -<a href="src/defint.cpp.html"> src</a> - -<p> -<h1><tt><a name="deg">deg(<i>p,x</i>)</a></tt></h1> -Returns the degree of polynomial p(x). -<a href="src/degree.cpp.html">src</a> - -<p> -<h1><tt><a name="denominator">denominator(<i>x</i>)</a></tt></h1> -Returns the denominator of expression x. -<a href="src/denominator.cpp.html">src</a> - -<p> -<h1><tt><a name="det">det(<i>m</i>)</a></tt></h1> -Returns the determinant of matrix m. -<a href="src/det.cpp.html">src</a> - -<p> -<h1><tt><a name="dim">dim(<i>a,n</i>)</a></tt></h1> -Returns the cardinality of the nth index of tensor "a". -<a href="src/eval.cpp.html#eval_dim">src</a> - -<p> -<h1><tt><a name="do">do(<i>a,b,...</i>)</a></tt></h1> -Evaluates each argument from left to right. -Returns the result of the last argument. -<a href="src/eval.cpp.html#eval_do">src</a> - -<p> -<h1><tt><a name="dot">dot(<i>a,b,...</i>)</a></tt></h1> -Returns the dot or inner product of tensors. -<a href="src/inner.cpp.html">src</a> - -<p> -<h1><tt><a name="draw">draw(<i>f,x</i>)</a></tt></h1> -Draws a graph of f(x). -Drawing ranges can be set with xrange and yrange. -<a href="src/draw.cpp.html">src</a> - -<!-- -<p> -<h1><tt><a name="eigen">eigen(<i>m</i>)</a></tt></h1> -<h1><tt>eigenval(<i>m</i>)</tt></h1> -<h1><tt>eigenvec(<i>m</i>)</tt></h1> -These functions compute eigenvalues and eigenvectors numerically. -Matrix m must be both numerical and symmetric. -The eigenval function returns a matrix with the eigenvalues along -the diagonal. -The eigenvec function returns a matrix with the eigenvectors arranged as row -vectors. -The eigen function does not return anything but stores the eigenvalue matrix -in D and the eigenvector matrix in Q. -<p> -Example 1. Check the relation AX = lambda X where lambda is an eigenvalue and -X is the associated eigenvector. -<pre> -<i>Enter</i> - - A = hilbert(3) - - eigen(A) - - lambda = D[1,1] - - X = Q[1] - - dot(A,X) - lambda X - -<i>Result</i> - - -1.16435e-14 - - -6.46705e-15 - - -4.55191e-15 -</pre> -<p> -Example 2: Check the relation A = Q<sup>T</sup>DQ. -<pre> -<i>Enter</i> - - A - dot(transpose(Q),D,Q) - -<i>Result</i> - - 6.27365e-12 -1.58236e-11 1.81902e-11 - - -1.58236e-11 -1.95365e-11 2.56514e-12 - - 1.81902e-11 2.56514e-12 1.32627e-11 -</pre> ---> - -<p> -<h1><tt><a name="erf">erf(<i>x</i>)</a></tt></h1> -Error function of x. -<a href="src/erf.cpp.html">src</a> - -<p> -<h1><tt><a name="erfc">erfc(<i>x</i>)</a></tt></h1> -Complementary error function of x. -<a href="src/erfc.cpp.html">src</a> - -<p> -<h1><tt><a name="eval">eval(<i>f,x,a</i>)</a></tt></h1> -Returns f evaluated at x=a. -<a href="src/eval.cpp.html#eval_eval">src</a> - -<p> -<h1><tt><a name="exp">exp(<i>x</i>)</a></tt></h1> -Returns the exponential of x. -<a href="src/eval.cpp.html#eval_exp">src</a> - -<p> -<h1><tt><a name="expand">expand(<i>r,x</i>)</a></tt></h1> -Returns the partial fraction expansion of the ratio of polynomials r in x. -<a href="src/expand.cpp.html">src</a> - -<p> -<h1><tt><a name="expcos">expcos(<i>x</i>)</a></tt></h1> -Returns the exponential cosine of x. -<a href="src/expcos.cpp.html">src</a> - -<p> -<h1><tt><a name="expsin">expsin(<i>x</i>)</a></tt></h1> -Returns the exponential sine of x. -<a href="src/expsin.cpp.html">src</a> - -<p> -<h1><tt><a name="factor">factor(<i>n</i>)</a></tt></h1> -Factors integer n. -<a href="src/factor.cpp.html">src</a> - -<p> -<h1><tt>factor(<i>p,x</i>)</tt></h1> -Factors polynomial p of x. -The x can be omitted for polynomials in x. -The polynomial should be factorable over integers. -The argument list can be extended for multivariate polynomials. -For example, factor(p,x,y) factors p over x and then over y. -<a href="src/factorpoly.cpp.html">src</a> - -<p> -<h1><tt><a name="factorial">factorial(<i>x</i>)</a></tt></h1> -Can be entered as x! -<a href="src/factorial.cpp.html">src</a> - -<p> -<h1><tt><a name="filter">filter(<i>f,a,b,...</i>)</a></tt></h1> -Returns f excluding any terms containing a, b, etc. -<a href="src/filter.cpp.html">src</a> - -<p> -<h1><tt><a name="float">float(<i>x</i>)</a></tt></h1> -Converts rational numbers and integers to floating point values. -The symbol pi is also converted. -<a href="src/float.cpp.html">src</a> - -<p> -<h1><tt><a name="floor">floor(<i>x</i>)</a></tt></h1> -Returns the largest integer not greater than x. -<a href="src/floor.cpp.html">src</a> - -<p> -<h1><tt><a name="for">for(<i>i,j,k,a,b,...</i>)</a></tt></h1> -For i equals j through k evaluate a, b, etc. -<a href="src/for.cpp.html">src</a> - -<p> -<h1><tt><a name="gcd">gcd(<i>a,b,...</i>)</a></tt></h1> -Returns the greatest common divisor. -<a href="src/gcd.cpp.html">src</a> - -<p> -<h1><tt><a name="hermite">hermite(<i>x,n</i>)</a></tt></h1> -Returns the nth Hermite polynomial in x. -<a href="src/hermite.cpp.html">src</a> - -<p> -<h1><tt><a name="hilbert">hilbert(<i>n</i>)</a></tt></h1> -Returns an n by n Hilbert matrix. -<a href="src/hilbert.cpp.html">src</a> - -<p> -<h1><tt><a name="imag">imag(<i>z</i>)</a></tt></h1> -Returns the imaginary part of complex z. -<a href="src/imag.cpp.html">src</a> - -<p> -<h1><tt><a name="inner">inner(<i>a,b,...</i>)</a></tt></h1> -Returns the inner product of tensors. -Same as the dot product. -<a href="src/inner.cpp.html">src</a> - -<p> -<h1><tt><a name="integral">integral(<i>f,x</i>)</a></tt></h1> -Returns the integral of f with respect to x. -<a href="src/integral.cpp.html">src</a> - -<p> -<h1><tt><a name="inv">inv(<i>m</i>)</a></tt></h1> -Returns the inverse of matrix m. -<a href="src/inv.cpp.html">src</a> - -<p> -<h1><tt><a name="isprime">isprime(<i>n</i>)</a></tt></h1> -Returns 1 if n is a prime number, returns zero otherwise. -<a href="src/isprime.cpp.html">src</a> - -<p> -<h1><tt><a name="laguerre">laguerre(<i>x,n,a</i>)</a></tt></h1> -Returns the nth Laguerre polynomial in x. -If "a" is omitted then a=0 is used. -<a href="src/laguerre.cpp.html">src</a> - -<p> -<h1><tt><a name="lcm">lcm(<i>a,b,...</i>)</a></tt></h1> -Returns the least common multiple. -<a href="src/lcm.cpp.html">src</a> - -<p> -<h1><tt><a name="leading">leading(<i>p,x</i>)</a></tt></h1> -Returns the leading coefficient of polynomial p in x. -<a href="src/leading.cpp.html">src</a> - -<p> -<h1><tt><a name="legendre">legendre(<i>x,n,m</i>)</a></tt></h1> -Returns the nth Legendre polynomial in x. -If m is omitted then m=0 is used. -<a href="src/legendre.cpp.html">src</a> - -<p> -<h1><tt><a name="log">log(<i>x</i>)</a></tt></h1> -Returns the natural logarithm of x. -<a href="src/log.cpp.html">src</a> - -<p> -<h1><tt><a name="mag">mag(<i>z</i>)</a></tt></h1> -Returns the magnitude of complex z. -<a href="src/mag.cpp.html">src</a> - -<p> -<h1><tt><a name="mod">mod(<i>a,b</i>)</a></tt></h1> -Returns the remainder of the result of "a" divided by b. -<a href="src/mod.cpp.html">src</a> - -<p> -<h1><tt><a name="not">not(<i>x</i>)</a></tt></h1> -Returns the logical negation of x. -<a href="src/test.cpp.html#eval_not">src</a> - -<p> -<h1><tt><a name="nroots">nroots(<i>p,x</i>)</a></tt></h1> -Returns all of the roots, both real and complex, -of polynomial p in x. -The roots are computed numerically. -The coefficients of p can be real or complex. -<a href="src/nroots.cpp.html">src</a> - -<p> -<h1><tt><a name="numerator">numerator(<i>x</i>)</a></tt></h1> -Returns the numerator of expression x. -<a href="src/numerator.cpp.html">src</a> - -<p> -<h1><tt><a name="or">or(<i>a,b,...</i>)</a></tt></h1> -Logical-or of predicate expressions. -<a href="src/test.cpp.html#eval_or">src</a> - -<p> -<h1><tt><a name="outer">outer(<i>a,b,...</i>)</a></tt></h1> -Returns the outer product of tensors. -Also known as the tensor product. -<a href="src/outer.cpp.html">src</a> - -<p> -<h1><tt><a name="polar">polar(<i>z</i>)</a></tt></h1> -Returns complex z in polar form. -<a href="src/polar.cpp.html">src</a> - -<p> -<h1><tt><a name="prime">prime(<i>n</i>)</a></tt></h1> -Returns the nth prime number. -The domain of n is 1 to 10000. -<a href="src/prime.cpp.html">src</a> - -<p> -<h1><tt><a name="print">print(<i>a,b,...</i>)</a></tt></h1> -Evaluate expressions and print the results. -Useful for printing from inside a "for" loop. -<a href="src/eval.cpp.html#eval_print">src</a> - -<p> -<h1><tt><a name="product">product(<i>i,j,k,f</i>)</a></tt></h1> -For i equals j through k evaluate f. -Returns the product of all f. -<a href="src/product.cpp.html">src</a> - -<p> -<h1><tt><a name="quote">quote(<i>x</i>)</a></tt></h1> -Returns expression x without evaluating it first. -<a href="src/eval.cpp.html#eval_quote">src</a> - -<p><h1><tt><a name="quotient">quotient(<i>p,q,x</i>)</a></tt></h1> -Returns the quotient of polynomial p(x) over q(x). -The last argument can be omitted for polynomials in x. -The remainder can be calculated by p-q*quotient(p,q). -<a href="src/quotient.cpp.html">src</a> - -<p> -<h1><tt><a name="rank">rank(<i>a</i>)</a></tt></h1> -Returns the number of indices that tensor "a" has. -<a href="src/eval.cpp.html#eval_rank">src</a> - -<p> -<h1><tt><a name="rationalize">rationalize(<i>x</i>)</a></tt></h1> -Returns x with everything over a common denominator. -<a href="src/rationalize.cpp.html">src</a> - -<p> -<h1><tt><a name="real">real(<i>z</i>)</a></tt></h1> -Returns the real part of complex z. -<a href="src/real.cpp.html">src</a> - -<p> -<h1><tt><a name="rect">rect(<i>z</i>)</a></tt></h1> -Returns complex z in rectangular form. -<a href="src/rect.cpp.html">src</a> - -<p> -<h1><tt><a name="roots">roots(<i>p,x</i>)</a></tt></h1> -Returns the values of x such that p(x)=0. -The polynomial p should be factorable over integers. -Returns a vector for multiple roots. -<a href="src/roots.cpp.html">src</a> - -<p> -<h1><tt><a name="simplify">simplify(<i>x</i>)</a></tt></h1> -Returns x in a simpler form. -<a href="src/simplify.cpp.html">src</a> - -<p> -<h1><tt><a name="sin">sin(<i>x</i>)</a></tt></h1> -Returns the sine of x. -<a href="src/sin.cpp.html">src</a> - -<p> -<h1><tt><a name="sinh">sinh(<i>x</i>)</a></tt></h1> -Returns the hyperbolic sine of x. -<a href="src/sinh.cpp.html">src</a> - -<p> -<h1><tt><a name="sqrt">sqrt(<i>x</i>)</a></tt></h1> -Returns the square root of x. -<a href="src/eval.cpp.html#eval_sqrt">src</a> - -<p> -<h1><tt><a name="stop">stop()</a></tt></h1> -In a script, it does what it says. -<a href="src/eval.cpp.html#eval_stop">src</a> - -<p> -<h1><tt><a name="subst">subst(<i>a,b,c</i>)</a></tt></h1> -Substitutes "a" for b in c and returns the result. -<a href="src/subst.cpp.html">src</a> - -<p> -<h1><tt><a name="sum">sum(<i>i,j,k,f</i>)</a></tt></h1> -For i equals j through k evaluate f. -Returns the sum of all f. -<a href="src/sum.cpp.html">src</a> - -<p> -<h1><tt><a name="tan">tan(<i>x</i>)</a></tt></h1> -Returns the tangent of <i>x</i>. -<a href="src/tan.cpp.html">src</a> - -<p> -<h1><tt><a name="tanh">tanh(<i>x</i>)</a></tt></h1> -Returns the hyperbolic tangent of <i>x</i>. -<a href="src/tanh.cpp.html">src</a> - -<p> -<h1><tt><a name="taylor">taylor(<i>f,x,n,a</i>)</a></tt></h1> -Returns the Taylor expansion of f(x) around x=a. -If "a" is omitted then a=0 is used. -The argument n is the degree of the expansion. -<a href="src/taylor.cpp.html">src</a> - -<p><h1><tt><a name="test">test(<i>a,b,c,d,...</i>)</a></tt></h1> -If "a" is true then b is returned -else if c is true then d is returned, etc. -If the number of arguments is odd then the last argument is returned -when all else fails. -<a href="src/test.cpp.html">src</a> - -<p> -<h1><tt><a name="transpose">transpose(<i>a,i,j</i>)</a></tt></h1> -Returns the transpose of "a" with respect to indices i and j. -If i and j are omitted then 1 and 2 are used. -Hence a matrix can be transposed with a single argument. -<a href="src/transpose.cpp.html">src</a> - -<p> -<h1><tt><a name="unit">unit(<i>n</i>)</a></tt></h1> -Returns an n by n identity matrix. -<a href="src/eval.cpp.html#eval_unit">src</a> - -<p> -<h1><tt><a name="zero">zero(<i>i,j,...</i>)</a></tt></h1> -Returns a null tensor with dimensions i, j, etc. -Useful for creating a tensor and then setting the component values. -<a href="src/zero.cpp.html">src</a> - -<p> -<a href="http://sourceforge.net"><img src="http://sflogo.sourceforge.net/sflogo.php?group_id=103462&type=2" width="125" height="37" border="0" alt="SourceForge.net Logo" /></a> - -</tt> -</body> -</html> +<html> +<head> +</head> +<body> +<tt> + +<img src="man.jpg"></td> +<p> +<a href="Eigenmath.pdf">Download Eigenmath.pdf</a> + +<p> +<hr> + +<p> +Example scripts + +<br><a href="examples/quantum-harmonic-oscillator.txt">quantum harmonic oscillator</a> + +<br><a href="examples/hydrogen-wavefunctions.txt">hydrogen wavefunctions</a> + +<br><a href="examples/gamma-matrix-algebra.txt">gamma matrix algebra</a> + +<br><a href="examples/free-particle-dirac-equation.txt">free particle dirac equation</a> + +<br><a href="examples/maxwell-in-tensor-form.txt">maxwell in tensor form</a> + +<br><a href="examples/static-spherical-metric.txt">static spherical metric</a> + +<br><a href="examples/bondi-metric.txt">bondi metric</a> + +<br><a href="examples/circular-polarization.txt">circular polarization</a> + +<br><a href="examples/elliptical-polarization.txt">elliptical polarization</a> + +<br><a href="examples/vector-calculus.txt">vector calculus demo</a> + +<br><a href="examples/rotation-matrix.txt">rotation matrix demo</a> + +<p> +<hr> + +<p> +<table cellspacing=20><tr><td valign="top"><tt> + +<a href="#abs">abs</a><br> +<a href="#adj">adj</a><br> +<a href="#and">and</a><br> +<a href="#arccos">arccos</a><br> +<a href="#arccosh">arccosh</a><br> +<a href="#arcsin">arcsin</a><br> +<a href="#arcsinh">arcsinh</a><br> +<a href="#arctan">arctan</a><br> +<a href="#arctanh">arctanh</a><br> +<a href="#arg">arg</a><br> +<a href="#ceiling">ceiling</a><br> +<a href="#check">check</a><br> +<a href="#choose">choose</a><br> + +</tt></td><td valign="top"><tt> + +<a href="#circexp">circexp</a><br> +<a href="#coeff">coeff</a><br> +<a href="#cofactor">cofactor</a><br> +<a href="#conj">conj</a><br> +<a href="#contract">contract</a><br> +<a href="#cos">cos</a><br> +<a href="#cosh">cosh</a><br> +<a href="#cross">cross</a><br> +<a href="#curl">curl</a><br> +<a href="#d">d</a><br> +<a href="#defint">defint</a><br> +<a href="#deg">deg</a><br> +<a href="#denominator">denominator</a><br> + +</tt></td><td valign="top"><tt> + +<a href="#det">det</a><br> +<a href="#dim">dim</a><br> +<a href="#do">do</a><br> +<a href="#dot">dot</a><br> +<a href="#draw">draw</a><br> +<a href="#erf">erf</a><br> +<a href="#erfc">erfc</a><br> +<a href="#eval">eval</a><br> +<a href="#exp">exp</a><br> +<a href="#expand">expand</a><br> +<a href="#expcos">expcos</a><br> +<a href="#expsin">expsin</a><br> +<a href="#factor">factor</a><br> + +</tt></td><td valign="top"><tt> + +<a href="#factorial">factorial</a><br> +<a href="#filter">filter</a><br> +<a href="#float">float</a><br> +<a href="#floor">floor</a><br> +<a href="#for">for</a><br> +<a href="#gcd">gcd</a><br> +<a href="#hermite">hermite</a><br> +<a href="#hilbert">hilbert</a><br> +<a href="#imag">imag</a><br> +<a href="#inner">inner</a><br> +<a href="#integral">integral</a><br> +<a href="#inv">inv</a><br> +<a href="#isprime">isprime</a><br> + +</tt></td><td valign="top"><tt> + +<a href="#laguerre">laguerre</a><br> +<a href="#lcm">lcm</a><br> +<a href="#leading">leading</a><br> +<a href="#legendre">legendre</a><br> +<a href="#log">log</a><br> +<a href="#mag">mag</a><br> +<a href="#mod">mod</a><br> +<a href="#not">not</a><br> +<a href="#nroots">nroots</a><br> +<a href="#numerator">numerator</a><br> +<a href="#or">or</a><br> +<a href="#outer">outer</a><br> +<a href="#polar">polar</a><br> + +</tt></td><td valign="top"><tt> + +<a href="#prime">prime</a><br> +<a href="#print">print</a><br> +<a href="#product">product</a><br> +<a href="#quote">quote</a><br> +<a href="#quotient">quotient</a><br> +<a href="#rank">rank</a><br> +<a href="#rationalize">rationalize</a><br> +<a href="#real">real</a><br> +<a href="#rect">rect</a><br> +<a href="#roots">roots</a><br> +<a href="#simplify">simplify</a><br> +<a href="#sin">sin</a><br> +<a href="#sinh">sinh</a><br> + +</tt></td><td valign="top"><tt> + +<a href="#sqrt">sqrt</a><br> +<a href="#stop">stop</a><br> +<a href="#subst">subst</a><br> +<a href="#sum">sum</a><br> +<a href="#tan">tan</a><br> +<a href="#tanh">tanh</a><br> +<a href="#taylor">taylor</a><br> +<a href="#test">test</a><br> +<a href="#transpose">transpose</a><br> +<a href="#unit">unit</a><br> +<a href="#zero">zero</a><br> + +</tt></td></tr></table> + +<p> +<hr> + +<p> +<h1><tt><a name="abs">abs(<i>x</i>)</a></tt></h1> +Returns the absolute value or vector length of x. +<a href="src/abs.cpp.html">src</a> + +<p> +<h1><tt><a name="adj">adj(<i>m</i>)</a></tt></h1> +Returns the adjunct of matrix m. +The inverse of m is equal to adj(m) divided by det(m). +<a href="src/adj.cpp.html">src</a> + +<p><h1><tt><a name="and">and(<i>a,b,...</i>)</a></tt></h1> +Logical-and of predicate expressions. +<a href="src/test.cpp.html#eval_and">src</a> + +<p> +<h1><tt><a name="arccos">arccos(<i>x</i>)</a></tt></h1> +Returns the inverse cosine of x. +<a href="src/arccos.cpp.html">src</a> + +<p> +<h1><tt><a name="arccosh">arccosh(<i>x</i>)</a></tt></h1> +Returns the inverse hyperbolic cosine of x. +<a href="src/arccosh.cpp.html">src</a> + +<p> +<h1><tt><a name="arcsin">arcsin(<i>x</i>)</a></tt></h1> +Returns the inverse sine of x. +<a href="src/arcsin.cpp.html">src</a> + +<p> +<h1><tt><a name="arcsinh">arcsinh(<i>x</i>)</a></tt></h1> +Returns the inverse hyperbolic sine of x. +<a href="src/arcsinh.cpp.html">src</a> + +<p> +<h1><tt><a name="arctan">arctan(<i>x</i>)</a></tt></h1> +Returns the inverse tangent of x. +<a href="src/arctan.cpp.html">src</a> + +<p> +<h1><tt><a name="arctanh">arctanh(<i>x</i>)</a></tt></h1> +Returns the inverse hyperbolic tangent of x. +<a href="src/arctanh.cpp.html">src</a> + +<p> +<h1><tt><a name="arg">arg(<i>z</i>)</a></tt></h1> +Returns the angle of complex z. +<a href="src/arg.cpp.html">src</a> + +<p> +<h1><tt><a name="ceiling">ceiling(<i>x</i>)</a></tt></h1> +Returns the smallest integer not less than x. +<a href="src/ceiling.cpp.html">src</a> + +<p> +<h1><tt><a name="check">check(<i>x</i>)</a></tt></h1> +If x is true then continue, else stop. +<a href="src/eval.cpp.html#eval_check">src </a> + +<p> +<h1><tt><a name="choose">choose(<i>n,k</i>)</a></tt></h1> +Returns the number of combinations of n items taken k at a time. +<a href="src/choose.cpp.html">src</a> + +<p> +<h1><tt><a name="circexp">circexp(<i>x</i>)</a></tt></h1> +Returns expression x with circular and hyperbolic functions converted to exponential forms. +Sometimes this will simplify an expression. +<a href="src/circexp.cpp.html">src</a> + +<p> +<h1><tt><a name="coeff">coeff(<i>p,x,n</i>)</a></tt></h1> +Returns the coefficient of x to the n in polynomial p. +The x argument can be omitted for polynomials in x. +<a href="src/coeff.cpp.html">src</a> + +<p> +<h1><tt><a name="cofactor">cofactor(<i>m,i,j</i>)</a></tt></h1> +Returns the cofactor of m for row i and column j. +<a href="src/cofactor.cpp.html">src</a> + +<p> +<h1><tt><a name="conj">conj(<i>z</i>)</a></tt></h1> +Returns the complex conjugate of z. +<a href="src/conj.cpp.html">src</a> + +<p> +<h1><tt><a name="contract">contract(<i>a,i,j</i>)</a></tt></h1> +Returns "a" summed over indices i and j. +If i and j are omitted then 1 and 2 are used. +contract(m) is equivalent to the trace of matrix m. +<a href="src/contract.cpp.html">src</a> + +<p> +<h1><tt><a name="cos">cos(<i>x</i>)</a></tt></h1> +Returns the cosine of x. +<a href="src/cos.cpp.html">src</a> + +<p> +<h1><tt><a name="cosh">cosh(<i>x</i>)</a></tt></h1> +Returns the hyperbolic cosine of x. +<a href="src/cosh.cpp.html">src</a> + +<p> +<h1><tt><a name="cross">cross(<i>u,v</i>)</a></tt></h1> +Returns the cross product of vectors u and v. + +<p> +<h1><tt><a name="curl">curl(<i>u</i>)</a></tt></h1> +Returns the curl of vector u. + +<p> +<h1><tt><a name="d">d(<i>f,x</i>)</a></tt></h1> +Returns the partial derivative of f with respect to x. +<a href="src/derivative.cpp.html">src</a> + +<p> +<h1><tt><a name="defint">defint(<i>f,x,a,b</i>)</a></tt></h1> +Returns the definite integral of f with respect to x +evaluated from "a" to b. +The argument list can be extended for multiple integrals. +For example, defint(f,x,a,b,y,c,d). +<a href="src/defint.cpp.html"> src</a> + +<p> +<h1><tt><a name="deg">deg(<i>p,x</i>)</a></tt></h1> +Returns the degree of polynomial p(x). +<a href="src/degree.cpp.html">src</a> + +<p> +<h1><tt><a name="denominator">denominator(<i>x</i>)</a></tt></h1> +Returns the denominator of expression x. +<a href="src/denominator.cpp.html">src</a> + +<p> +<h1><tt><a name="det">det(<i>m</i>)</a></tt></h1> +Returns the determinant of matrix m. +<a href="src/det.cpp.html">src</a> + +<p> +<h1><tt><a name="dim">dim(<i>a,n</i>)</a></tt></h1> +Returns the cardinality of the nth index of tensor "a". +<a href="src/eval.cpp.html#eval_dim">src</a> + +<p> +<h1><tt><a name="do">do(<i>a,b,...</i>)</a></tt></h1> +Evaluates each argument from left to right. +Returns the result of the last argument. +<a href="src/eval.cpp.html#eval_do">src</a> + +<p> +<h1><tt><a name="dot">dot(<i>a,b,...</i>)</a></tt></h1> +Returns the dot or inner product of tensors. +<a href="src/inner.cpp.html">src</a> + +<p> +<h1><tt><a name="draw">draw(<i>f,x</i>)</a></tt></h1> +Draws a graph of f(x). +Drawing ranges can be set with xrange and yrange. +<a href="src/draw.cpp.html">src</a> + +<!-- +<p> +<h1><tt><a name="eigen">eigen(<i>m</i>)</a></tt></h1> +<h1><tt>eigenval(<i>m</i>)</tt></h1> +<h1><tt>eigenvec(<i>m</i>)</tt></h1> +These functions compute eigenvalues and eigenvectors numerically. +Matrix m must be both numerical and symmetric. +The eigenval function returns a matrix with the eigenvalues along +the diagonal. +The eigenvec function returns a matrix with the eigenvectors arranged as row +vectors. +The eigen function does not return anything but stores the eigenvalue matrix +in D and the eigenvector matrix in Q. +<p> +Example 1. Check the relation AX = lambda X where lambda is an eigenvalue and +X is the associated eigenvector. +<pre> +<i>Enter</i> + + A = hilbert(3) + + eigen(A) + + lambda = D[1,1] + + X = Q[1] + + dot(A,X) - lambda X + +<i>Result</i> + + -1.16435e-14 + + -6.46705e-15 + + -4.55191e-15 +</pre> +<p> +Example 2: Check the relation A = Q<sup>T</sup>DQ. +<pre> +<i>Enter</i> + + A - dot(transpose(Q),D,Q) + +<i>Result</i> + + 6.27365e-12 -1.58236e-11 1.81902e-11 + + -1.58236e-11 -1.95365e-11 2.56514e-12 + + 1.81902e-11 2.56514e-12 1.32627e-11 +</pre> +--> + +<p> +<h1><tt><a name="erf">erf(<i>x</i>)</a></tt></h1> +Error function of x. +<a href="src/erf.cpp.html">src</a> + +<p> +<h1><tt><a name="erfc">erfc(<i>x</i>)</a></tt></h1> +Complementary error function of x. +<a href="src/erfc.cpp.html">src</a> + +<p> +<h1><tt><a name="eval">eval(<i>f,x,a</i>)</a></tt></h1> +Returns f evaluated at x=a. +<a href="src/eval.cpp.html#eval_eval">src</a> + +<p> +<h1><tt><a name="exp">exp(<i>x</i>)</a></tt></h1> +Returns the exponential of x. +<a href="src/eval.cpp.html#eval_exp">src</a> + +<p> +<h1><tt><a name="expand">expand(<i>r,x</i>)</a></tt></h1> +Returns the partial fraction expansion of the ratio of polynomials r in x. +<a href="src/expand.cpp.html">src</a> + +<p> +<h1><tt><a name="expcos">expcos(<i>x</i>)</a></tt></h1> +Returns the exponential cosine of x. +<a href="src/expcos.cpp.html">src</a> + +<p> +<h1><tt><a name="expsin">expsin(<i>x</i>)</a></tt></h1> +Returns the exponential sine of x. +<a href="src/expsin.cpp.html">src</a> + +<p> +<h1><tt><a name="factor">factor(<i>n</i>)</a></tt></h1> +Factors integer n. +<a href="src/factor.cpp.html">src</a> + +<p> +<h1><tt>factor(<i>p,x</i>)</tt></h1> +Factors polynomial p of x. +The x can be omitted for polynomials in x. +The polynomial should be factorable over integers. +The argument list can be extended for multivariate polynomials. +For example, factor(p,x,y) factors p over x and then over y. +<a href="src/factorpoly.cpp.html">src</a> + +<p> +<h1><tt><a name="factorial">factorial(<i>x</i>)</a></tt></h1> +Can be entered as x! +<a href="src/factorial.cpp.html">src</a> + +<p> +<h1><tt><a name="filter">filter(<i>f,a,b,...</i>)</a></tt></h1> +Returns f excluding any terms containing a, b, etc. +<a href="src/filter.cpp.html">src</a> + +<p> +<h1><tt><a name="float">float(<i>x</i>)</a></tt></h1> +Converts rational numbers and integers to floating point values. +The symbol pi is also converted. +<a href="src/float.cpp.html">src</a> + +<p> +<h1><tt><a name="floor">floor(<i>x</i>)</a></tt></h1> +Returns the largest integer not greater than x. +<a href="src/floor.cpp.html">src</a> + +<p> +<h1><tt><a name="for">for(<i>i,j,k,a,b,...</i>)</a></tt></h1> +For i equals j through k evaluate a, b, etc. +<a href="src/for.cpp.html">src</a> + +<p> +<h1><tt><a name="gcd">gcd(<i>a,b,...</i>)</a></tt></h1> +Returns the greatest common divisor. +<a href="src/gcd.cpp.html">src</a> + +<p> +<h1><tt><a name="hermite">hermite(<i>x,n</i>)</a></tt></h1> +Returns the nth Hermite polynomial in x. +<a href="src/hermite.cpp.html">src</a> + +<p> +<h1><tt><a name="hilbert">hilbert(<i>n</i>)</a></tt></h1> +Returns an n by n Hilbert matrix. +<a href="src/hilbert.cpp.html">src</a> + +<p> +<h1><tt><a name="imag">imag(<i>z</i>)</a></tt></h1> +Returns the imaginary part of complex z. +<a href="src/imag.cpp.html">src</a> + +<p> +<h1><tt><a name="inner">inner(<i>a,b,...</i>)</a></tt></h1> +Returns the inner product of tensors. +Same as the dot product. +<a href="src/inner.cpp.html">src</a> + +<p> +<h1><tt><a name="integral">integral(<i>f,x</i>)</a></tt></h1> +Returns the integral of f with respect to x. +<a href="src/integral.cpp.html">src</a> + +<p> +<h1><tt><a name="inv">inv(<i>m</i>)</a></tt></h1> +Returns the inverse of matrix m. +<a href="src/inv.cpp.html">src</a> + +<p> +<h1><tt><a name="isprime">isprime(<i>n</i>)</a></tt></h1> +Returns 1 if n is a prime number, returns zero otherwise. +<a href="src/isprime.cpp.html">src</a> + +<p> +<h1><tt><a name="laguerre">laguerre(<i>x,n,a</i>)</a></tt></h1> +Returns the nth Laguerre polynomial in x. +If "a" is omitted then a=0 is used. +<a href="src/laguerre.cpp.html">src</a> + +<p> +<h1><tt><a name="lcm">lcm(<i>a,b,...</i>)</a></tt></h1> +Returns the least common multiple. +<a href="src/lcm.cpp.html">src</a> + +<p> +<h1><tt><a name="leading">leading(<i>p,x</i>)</a></tt></h1> +Returns the leading coefficient of polynomial p in x. +<a href="src/leading.cpp.html">src</a> + +<p> +<h1><tt><a name="legendre">legendre(<i>x,n,m</i>)</a></tt></h1> +Returns the nth Legendre polynomial in x. +If m is omitted then m=0 is used. +<a href="src/legendre.cpp.html">src</a> + +<p> +<h1><tt><a name="log">log(<i>x</i>)</a></tt></h1> +Returns the natural logarithm of x. +<a href="src/log.cpp.html">src</a> + +<p> +<h1><tt><a name="mag">mag(<i>z</i>)</a></tt></h1> +Returns the magnitude of complex z. +<a href="src/mag.cpp.html">src</a> + +<p> +<h1><tt><a name="mod">mod(<i>a,b</i>)</a></tt></h1> +Returns the remainder of the result of "a" divided by b. +<a href="src/mod.cpp.html">src</a> + +<p> +<h1><tt><a name="not">not(<i>x</i>)</a></tt></h1> +Returns the logical negation of x. +<a href="src/test.cpp.html#eval_not">src</a> + +<p> +<h1><tt><a name="nroots">nroots(<i>p,x</i>)</a></tt></h1> +Returns all of the roots, both real and complex, +of polynomial p in x. +The roots are computed numerically. +The coefficients of p can be real or complex. +<a href="src/nroots.cpp.html">src</a> + +<p> +<h1><tt><a name="numerator">numerator(<i>x</i>)</a></tt></h1> +Returns the numerator of expression x. +<a href="src/numerator.cpp.html">src</a> + +<p> +<h1><tt><a name="or">or(<i>a,b,...</i>)</a></tt></h1> +Logical-or of predicate expressions. +<a href="src/test.cpp.html#eval_or">src</a> + +<p> +<h1><tt><a name="outer">outer(<i>a,b,...</i>)</a></tt></h1> +Returns the outer product of tensors. +Also known as the tensor product. +<a href="src/outer.cpp.html">src</a> + +<p> +<h1><tt><a name="polar">polar(<i>z</i>)</a></tt></h1> +Returns complex z in polar form. +<a href="src/polar.cpp.html">src</a> + +<p> +<h1><tt><a name="prime">prime(<i>n</i>)</a></tt></h1> +Returns the nth prime number. +The domain of n is 1 to 10000. +<a href="src/prime.cpp.html">src</a> + +<p> +<h1><tt><a name="print">print(<i>a,b,...</i>)</a></tt></h1> +Evaluate expressions and print the results. +Useful for printing from inside a "for" loop. +<a href="src/eval.cpp.html#eval_print">src</a> + +<p> +<h1><tt><a name="product">product(<i>i,j,k,f</i>)</a></tt></h1> +For i equals j through k evaluate f. +Returns the product of all f. +<a href="src/product.cpp.html">src</a> + +<p> +<h1><tt><a name="quote">quote(<i>x</i>)</a></tt></h1> +Returns expression x without evaluating it first. +<a href="src/eval.cpp.html#eval_quote">src</a> + +<p><h1><tt><a name="quotient">quotient(<i>p,q,x</i>)</a></tt></h1> +Returns the quotient of polynomial p(x) over q(x). +The last argument can be omitted for polynomials in x. +The remainder can be calculated by p-q*quotient(p,q). +<a href="src/quotient.cpp.html">src</a> + +<p> +<h1><tt><a name="rank">rank(<i>a</i>)</a></tt></h1> +Returns the number of indices that tensor "a" has. +<a href="src/eval.cpp.html#eval_rank">src</a> + +<p> +<h1><tt><a name="rationalize">rationalize(<i>x</i>)</a></tt></h1> +Returns x with everything over a common denominator. +<a href="src/rationalize.cpp.html">src</a> + +<p> +<h1><tt><a name="real">real(<i>z</i>)</a></tt></h1> +Returns the real part of complex z. +<a href="src/real.cpp.html">src</a> + +<p> +<h1><tt><a name="rect">rect(<i>z</i>)</a></tt></h1> +Returns complex z in rectangular form. +<a href="src/rect.cpp.html">src</a> + +<p> +<h1><tt><a name="roots">roots(<i>p,x</i>)</a></tt></h1> +Returns the values of x such that p(x)=0. +The polynomial p should be factorable over integers. +Returns a vector for multiple roots. +<a href="src/roots.cpp.html">src</a> + +<p> +<h1><tt><a name="simplify">simplify(<i>x</i>)</a></tt></h1> +Returns x in a simpler form. +<a href="src/simplify.cpp.html">src</a> + +<p> +<h1><tt><a name="sin">sin(<i>x</i>)</a></tt></h1> +Returns the sine of x. +<a href="src/sin.cpp.html">src</a> + +<p> +<h1><tt><a name="sinh">sinh(<i>x</i>)</a></tt></h1> +Returns the hyperbolic sine of x. +<a href="src/sinh.cpp.html">src</a> + +<p> +<h1><tt><a name="sqrt">sqrt(<i>x</i>)</a></tt></h1> +Returns the square root of x. +<a href="src/eval.cpp.html#eval_sqrt">src</a> + +<p> +<h1><tt><a name="stop">stop()</a></tt></h1> +In a script, it does what it says. +<a href="src/eval.cpp.html#eval_stop">src</a> + +<p> +<h1><tt><a name="subst">subst(<i>a,b,c</i>)</a></tt></h1> +Substitutes "a" for b in c and returns the result. +<a href="src/subst.cpp.html">src</a> + +<p> +<h1><tt><a name="sum">sum(<i>i,j,k,f</i>)</a></tt></h1> +For i equals j through k evaluate f. +Returns the sum of all f. +<a href="src/sum.cpp.html">src</a> + +<p> +<h1><tt><a name="tan">tan(<i>x</i>)</a></tt></h1> +Returns the tangent of <i>x</i>. +<a href="src/tan.cpp.html">src</a> + +<p> +<h1><tt><a name="tanh">tanh(<i>x</i>)</a></tt></h1> +Returns the hyperbolic tangent of <i>x</i>. +<a href="src/tanh.cpp.html">src</a> + +<p> +<h1><tt><a name="taylor">taylor(<i>f,x,n,a</i>)</a></tt></h1> +Returns the Taylor expansion of f(x) around x=a. +If "a" is omitted then a=0 is used. +The argument n is the degree of the expansion. +<a href="src/taylor.cpp.html">src</a> + +<p><h1><tt><a name="test">test(<i>a,b,c,d,...</i>)</a></tt></h1> +If "a" is true then b is returned +else if c is true then d is returned, etc. +If the number of arguments is odd then the last argument is returned +when all else fails. +<a href="src/test.cpp.html">src</a> + +<p> +<h1><tt><a name="transpose">transpose(<i>a,i,j</i>)</a></tt></h1> +Returns the transpose of "a" with respect to indices i and j. +If i and j are omitted then 1 and 2 are used. +Hence a matrix can be transposed with a single argument. +<a href="src/transpose.cpp.html">src</a> + +<p> +<h1><tt><a name="unit">unit(<i>n</i>)</a></tt></h1> +Returns an n by n identity matrix. +<a href="src/eval.cpp.html#eval_unit">src</a> + +<p> +<h1><tt><a name="zero">zero(<i>i,j,...</i>)</a></tt></h1> +Returns a null tensor with dimensions i, j, etc. +Useful for creating a tensor and then setting the component values. +<a href="src/zero.cpp.html">src</a> + +</tt> + +<script type="text/javascript"> +var gaJsHost = (("https:" == document.location.protocol) ? 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