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George Weigt
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118
help.html
118
help.html
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@ -136,11 +136,6 @@ The inverse of m is equal to adj(m) divided by det(m).
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<p><h1><tt><a name="and">and(<i>a,b,...</i>)</a></tt></h1>
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Logical-and of predicate expressions.
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<pre>
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<i>Example</i>
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and(A=B,B=C)
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</pre>
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<p>
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<h1><tt><a name="arccos">arccos(<i>x</i>)</a></tt></h1>
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@ -177,20 +172,14 @@ Returns the smallest integer not less than x.
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<p>
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<h1><tt><a name="check">check(<i>x</i>)</a></tt></h1>
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If x is true then continue, else stop.
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<pre>
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<i>Example</i>
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check(A=B)
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</pre>
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<p>
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<h1><tt><a name="choose">choose(<i>n,k</i>)</a></tt></h1>
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Returns the number of combinations of n items taken k at a time,
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choose(n,k)=n!/(k!*(n-k)!)
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Returns the number of combinations of n items taken k at a time.
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<p>
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<h1><tt><a name="circexp">circexp(<i>x</i>)</a></tt></h1>
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Returns expression x with circular functions converted to exponential forms.
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Returns expression x with circular and hyperbolic functions converted to exponential forms.
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Sometimes this will simplify an expression.
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<p>
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@ -205,32 +194,12 @@ Returns the cofactor of m for row i and column j.
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<p>
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<h1><tt><a name="conj">conj(<i>z</i>)</a></tt></h1>
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Returns the complex conjugate of z.
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<pre>
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<i>Example</i>
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conj(3+4*i)
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</pre>
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<p>
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<h1><tt><a name="contract">contract(<i>a,i,j</i>)</a></tt></h1>
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Returns "a" summed over indices i and j.
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If i and j are omitted then 1 and 2 are used.
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<!--
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The following example shows how contract adds diagonal elements.
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<pre>
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<i>Enter</i>
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A = ((a,b),(c,d))
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contract(A,1,2)
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<i>Result</i>
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a + d
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</pre>
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-->
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<p>
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<h1><tt><a name="cos">cos(<i>x</i>)</a></tt></h1>
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Returns the cosine of x.
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@ -368,16 +337,7 @@ The polynomial should be factorable over integers.
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<p>
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<h1><tt><a name="factorial">factorial(<i>x</i>)</a></tt></h1>
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For example,
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<pre>
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<i>Enter</i>
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100!
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<i>Result</i>
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93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
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</pre>
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Can be entered as x!
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<p>
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<h1><tt><a name="filter">filter(<i>f,a,b,...</i>)</a></tt></h1>
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@ -385,17 +345,8 @@ Returns f excluding any terms containing a, b, etc.
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<p>
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<h1><tt><a name="float">float(<i>x</i>)</a></tt></h1>
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Converts rational numbers and integers to floating
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point values. The symbol pi is also converted.
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<pre>
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<i>Enter</i>
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float(100!)
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<i>Result</i>
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9.33262e+157
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</pre>
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Converts rational numbers and integers to floating point values.
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The symbol pi is also converted.
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<p>
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<h1><tt><a name="floor">floor(<i>x</i>)</a></tt></h1>
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@ -404,18 +355,6 @@ Returns the largest integer not greater than x.
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<p>
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<h1><tt><a name="for">for(<i>i,j,k,a,b,...</i>)</a></tt></h1>
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For i equals j through k evaluate a, b, etc.
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<pre>
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<i>Enter</i>
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x=0
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y=2
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for(k,1,9,x=sqrt(2+x),y=2*y/x)
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float(y)
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<i>Result</i>
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3.14159
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</pre>
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<p>
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<h1><tt><a name="gcd">gcd(<i>a,b,...</i>)</a></tt></h1>
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@ -467,17 +406,6 @@ If m is omitted then m=0 is used.
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<p>
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<h1><tt><a name="log">log(<i>x</i>)</a></tt></h1>
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Returns the natural logarithm of x.
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<!--
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<pre>
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<i>Enter</i>
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log(-10.0)
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<i>Result</i>
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2.30259 + i π
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</pre>
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-->
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<p>
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<h1><tt><a name="mag">mag(<i>z</i>)</a></tt></h1>
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@ -490,11 +418,6 @@ Returns the remainder of the result of "a" divided by b.
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<p>
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<h1><tt><a name="not">not(<i>x</i>)</a></tt></h1>
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Returns the logical negation of x.
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<pre>
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<i>Example</i>
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not(A=B)
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</pre>
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<p>
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<h1><tt><a name="numerator">numerator(<i>x</i>)</a></tt></h1>
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@ -503,11 +426,6 @@ Returns the numerator of expression x.
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<p>
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<h1><tt><a name="or">or(<i>a,b,...</i>)</a></tt></h1>
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Logical-or of predicate expressions.
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<pre>
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<i>Example</i>
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or(A=B,A=C)
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</pre>
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<p>
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<h1><tt><a name="outer">outer(<i>a,b,...</i>)</a></tt></h1>
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@ -517,22 +435,11 @@ Also known as the tensor product.
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<p>
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<h1><tt><a name="polar">polar(<i>z</i>)</a></tt></h1>
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Returns complex z in polar form.
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<!--
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<pre>
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<i>Enter</i>
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polar(1 + exp(i pi/3))
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<i>Result</i>
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1/6 1/2
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(-1) 3
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</pre>
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-->
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<p>
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<h1><tt><a name="prime">prime(<i>n</i>)</a></tt></h1>
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Returns the nth prime number, 1≤n≤10000.
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Returns the nth prime number.
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The domain of n is 1 to 10000.
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<p>
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<h1><tt><a name="print">print(<i>x</i>)</a></tt></h1>
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@ -616,17 +523,6 @@ Returns the hyperbolic tangent of <i>x</i>.
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Returns the Taylor expansion of f(x) around x=a.
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If "a" is omitted then a=0 is used.
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The argument n is the degree of the expansion.
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<pre>
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<i>Enter</i>
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taylor(1/cos(x),x,6)
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<i>Result</i>
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1 2 5 4 61 6
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1 + --- x + ---- x + ----- x
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2 24 720
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</pre>
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<p><h1><tt><a name="test">test(<i>a,b,c,d,...</i>)</a></tt></h1>
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If "a" is true then b is returned
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69
man.tex
69
man.tex
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@ -1,7 +1,7 @@
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\documentclass[12pt,openany]{report}
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\title{Eigenmath Manual}
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\author{George Weigt}
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\date{May 5, 2007}
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\date{May 12, 2007}
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\pagestyle{headings}
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\usepackage{graphicx}
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@ -313,8 +313,44 @@ The default range is $(-\pi,\pi)$.
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\noindent
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\includegraphics[scale=0.5]{circle2.png}
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\newpage
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\noindent
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Here are a couple of interesting curves and the code for drawing them.
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First is a lemniscate.
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\medskip
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\verb$clear$
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\verb$X=cos(t)/(1+sin(t)^2)$
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\verb$Y=sin(t)*cos(t)/(1+sin(t)^2)$
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\verb$draw(5*(X,Y))$
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\medskip
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\noindent
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\includegraphics[scale=0.5]{lemniscate.png}
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\medskip
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\noindent
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Next is a cardioid.
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\medskip
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\verb$r=(1+cos(t))/2$
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\verb$u=(cos(t),sin(t))$
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\verb$xrange=(-1,1)$
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\verb$yrange=(-1,1)$
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\verb$draw(r*u)$
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\medskip
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\noindent
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\includegraphics[scale=0.5]{cardioid.png}
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\newpage
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\chapter{Linear Algebra}
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@ -580,6 +616,37 @@ $${1\over8}\pi$$
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\newpage
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\noindent
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The following example demonstrates a technique for computing
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a line integral when the path is already parameterized.
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The task at hand is to compute\footnote{
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From a problem in {\it Advanced Calculus} by Wilfred Kaplan.}
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$$\int_C z\,dx+x\,dy+y\,dz$$
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where $C$ is the path
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$$x=2t+1,\qquad y=t^2,\qquad z=1+t^3,\qquad 0\le t\le 1$$
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The main idea is that we can rewrite the integrand with the following substitutions.
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$$dx=\left({dx\over dt}\right)dt,\qquad
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dy=\left({dy\over dt}\right)dt,\qquad
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dz=\left({dz\over dt}\right)dt$$
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Therefore in Eigenmath we have
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\medskip
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\verb$x=2t+1$
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\verb$y=t^2$
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\verb$z=1+t^3$
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\verb$f=z*d(x,t)+x*d(y,t)+y*d(z,t)$
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\verb$I=integral(f,t)$
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\verb$eval(I,t,1)-eval(I,t,0)$
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$$163\over30$$
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\newpage
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\chapter{Complex Numbers}
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\noindent
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