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The Maxima on-line user's manual

Algebra Calculator

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Radcan Calculator

Radcan

Function: radcan (<expr>) Simplifies <expr>, which can contain logs, exponentials, and radicals, by converting it into a form which is canonical over a large class of expressions and a given ordering of variables; that is, all functionally equivalent forms are mapped into a unique form. For a somewhat larger class of expressions, radcan produces a regular form. Two equivalent expressions in this class do not necessarily have the same appearance, but their difference can be simplified by radcan to zero.

f(x):=16*(1-x^5)/(1-x);
f(0.5);
gp(x):=(sqrt(f(x))+sum(x^k,k,2,28))/2;
gm(x):=(sqrt(f(x))-sum(x^k,k,2,28))/2;
float(subst(0.5,x,gp(x)*gm(x)));
tp(x):=taylor(gp(x),x,0,4);
float(tp(x));
tm(x):=taylor(gm(x),x,0,4);
float(tm(x));
float(subst(0.5,x,tp(x)));
float(subst(0.5,x,tm(x)));
h(x):=float(tp(x))^(1/3)-float(tm(x))^(1/3);
radcan(expand(float(ratsimp(h(x)))));
float(subst(0.5,x,h(x))/sqrt(3));

For some expressions radcan is quite time consuming. This is the cost of exploring certain relationships among the components of the expression for simplifications based on factoring and partial-fraction expansions of exponents.

Examples:

          (%i1) radcan((log(x+x^2)-log(x))^a/log(1+x)^(a/2));
                                                     a/2
          (%o1)                            log(x + 1)

          (%i2) radcan((log(1+2*a^x+a^(2*x))/log(1+a^x)));
          (%o2)                                  2

          (%i3) radcan((%e^x-1)/(1+%e^(x/2)));
                                               x/2
          (%o3)                              %e    - 1

There are also some inexact matches for radcan. Try ?? radcan to see them.

(%o1)                                true
(%i2) 

Radcan Example

Related Examples

radcan-sqrt

-sqrt(1-4*t)/(4*t-1);

radcan(%);

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radcan

radcan((2^10)^(1/3));

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radcan

radcan(Ri + (( (1/(C1...

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radcan

u : 2*(z-c);

v : 2*(z+c);

F : p*t^4 + u*t^3 + v...

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radcan-solve-subst

mye: (x^2-1)/(x-1)=1;

radcan(mye);

( (((subst( mye, x = ...

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radcan

eq1:radcan(((2*m)!*(3...

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radcan-sqrt

radcan(sqrt(4+(x^2))/...

Calculate

radcan-sin

radcan(sin(2*x));

Calculate

radcan-sqrt

radcan((x^7-3.5*x^6+1...

Calculate

radcan-sqrt

a : sqrt(r*s);

b : sqrt(s/r);

a1: a + 1/b;

Calculate