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%mathpiper,def="Simplify"
10 # Simplify(expr_IsList) <-- MapSingle("Simplify",expr);
15 # Simplify(Complex(_r,_i)) <-- Complex(Simplify(r),Simplify(i));
20 # Simplify((_xex) == (_yex)) <-- (Simplify(xex-yex) == 0);
20 # Simplify((_xex) > (_yex)) <-- (Simplify(xex-yex) > 0);
20 # Simplify((_xex) < (_yex)) <-- (Simplify(xex-yex) < 0);
20 # Simplify((_xex) >= (_yex)) <-- (Simplify(xex-yex) >= 0);
20 # Simplify((_xex) <= (_yex)) <-- (Simplify(xex-yex) <= 0);
20 # Simplify((_xex) !== (_yex)) <-- (Simplify(xex-yex) !== 0);
// conditionals
25 # Simplify(if (_a) _b) <-- "if" @ {Simplify(a), Simplify(b)};
25 # Simplify(_a else _b) <-- "else" @ {Simplify(a), Simplify(b)};
//Testing with Simplify(1+1/x)
50 # Simplify(_expr) <--
[
Local(s,g);
s := MultiSimp(Eval(expr));
If(IsRationalFunction(s) And ( Type(Numerator(s)) != "Numer") And ( Type(Denominator(s)) != "Denom"),
[
Echo("s ",s);
Echo("Numerator(s) ", Numerator(s));
Echo("Denominator(s) ", Denominator(s));
g := Gcd(Numerator(s),Denominator(s));
Echo("g ",g);
If( InVerboseMode(),
[
Show(10,expr);
Show(11,s);
Show(12,Equals(s,expr));
Show(13,g);
NewLine();
]
);
If( s=expr,
[
If( Equals(Numerator(expr),-Denominator(expr)), s := -1 );
/* And here one can put other simplifications, as they are developed */
],
[
s := Simplify((Numerator(expr)/g))/Simplify(Denominator(expr)/g);
If(InVerboseMode(),Tell(14,s));
]
);
s;
],
[
s;
]
);
];
10 # IsRationalFunction(x_IsRationalOrNumber) <-- False;
15 # IsRationalFunction(_x)_(Type(x)="/") <-- True;
60000 # IsRationalFunction(_x) <-- False;
%/mathpiper
%mathpiper_docs,name="Simplify",categories="User Functions;Expression Simplification"
*CMD Simplify --- try to simplify an expression
*STD
*CALL
Simplify(expr)
*PARMS
{expr} -- expression to simplify
*DESC
This function tries to simplify the expression {expr} as much
as possible. It does this by grouping powers within terms, and then
grouping similar terms.
*E.G.
In> a*b*a^2/b-a^3
Out> (b*a^3)/b-a^3;
In> Simplify(a*b*a^2/b-a^3)
Out> 0;
*SEE TrigSimpCombine, RadSimp
%/mathpiper_docs
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