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&amp;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>
+
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