### Related

##### denom-factor

H:(Wn*Wn)/(s*s+2*d*Wn...

H2:factor(H);

D:denom(H2);

Calculate

##### denom-diff

denom(diff(1/(A^4*(A^...

Calculate

##### denom-factor-num-ratsimp

%f[2,1]([1,1],[3/2],1...

P(k) := k + 1;

Q(k) := k + 3/2;

Calculate

##### denom-lhs-ratsimp-rhs-solve-subst

eq1: k*(psi*iQ+Ldiff*...

eq2: solve(eq1 = M, iQ);

eq3: iD^2+iQ^2;

Calculate

##### denom

denom((5*x)/(x^2-4));

Calculate

##### denom-factor-num-ratsimp-subst

T:ratsimp(2/(4*k+1)+2...

S:subst(k+1,k,T)/T*(-...

factor(num(S));

Calculate

##### denom-expand-factorial_expand-gamma-num-true

p(n,a,k):=1/(k!*(n-k)...

gamma_expand: true;

factorial_expand: true;

Calculate

##### denom-diff-linsolve-ratsimp-solve-sqrt

f(x):=(x-9/4)*sqrt(2*x);

solve(denom(f(x)=0,x));

nsleq:f(x)=0;

Calculate

a:5;

a;

a+3;

Calculate

##### denom-diff-ev-exp-exptsubst-ic1-lhs-logcontract-ode2-rhs-solve-subst

eq1 : 'diff(P,t) = P*...

gsoln : ode2(eq1, P,t...

gsoln : gsoln * denom...

Calculate

### denom

Run Example
(%i1)f(x):=(x^2-2*x)*exp(x);
2
(%o1)                      f(x) := (x  - 2 x) exp(x)
(%i2) solve(denom(f(x))=0);

solve: variable list is empty, continuing anyway.
(%o2)                                 []
(%i3) solve(f(x)=0,x);
x
(%o3)                       [x = 0, x = 2, %e  = 0]
(%i4) f(0);
(%o4)                                  0
(%i5) f(2);
(%o5)                                  0
(%i6) f1(x):=''(diff(f(x),x));
2          x               x
(%o6)               f1(x) := (x  - 2 x) %e  + (2 x - 2) %e
(%i7) 
Run Example
factorC(_f,_z):=block([s,n,m,fp,j],fp:1,/* This commented code was meant to use themore robust solver to_poly_solve, but I couldn't understand how to handle multiplicitiesss:args(to_poly_solve(_f,_z)),s:create_list(ss[k][1],k,1,length(ss)),*/s:solve(_f,_z),m:multiplicities,n:length(s),for j:1 thru n do  if lhs(s[j])#0  then fp:fp*(_z-(rhs(s[j])))^m[j], fp:fp*divide(_f,fp)[1],fp);
(%o1) factorC(_f, _z) := block([s, n, m, fp, j], fp : 1, s : solve(_f, _z),
m : multiplicities, n : length(s), for j thru n
m
j
do if lhs(s ) # 0 then fp : fp (_z - rhs(s ))  , fp : fp divide(_f, fp) , fp)
j                              j                            1
(%i2) partfracC(_f,_z):=block([d,fd],d:denom(_f),fd:factorC(d,_z),partfrac(1/fd,_z));
(%o2) partfracC(_f, _z) := block([d, fd], d : denom(_f), fd : factorC(d, _z),
1
partfrac(--, _z))
fd
(%i3) O:partfracC(1/(x^5-1)^4,x);
4 %i %pi           2 %i %pi             2 %i %pi
--------           --------           - --------
5                  5                    5
(%o3) (41992 %e         + 42160 %e         + 42076 %e
4 %i %pi                  4 %i %pi         2 %i %pi            4 %i %pi            4 %i %pi
- --------                  --------         --------          - --------            --------
5                         5                5                   5                   5
+ 41824 %e           + 42328)/((625 %e         - 625 %e         + 1875 %e           - 1875) (%e         x
- 1))
4 %i %pi          2 %i %pi            2 %i %pi            4 %i %pi
--------          --------          - --------          - --------
5                 5                   5                   5
+ (1082 %e         + 1018 %e         + 1114 %e           + 1114 %e
2 %i %pi           2 %i %pi           4 %i %pi
--------         - --------         - --------
5                  5                  5
+ 1082)/((- 1250 %e         + 625 %e           + 625 %e          )
4 %i %pi
--------
5           2
(%e         x - 1) )
4 %i %pi        2 %i %pi          2 %i %pi          4 %i %pi
--------        --------        - --------        - --------
5               5                 5                 5
28 %e         + 20 %e         + 12 %e           + 20 %e           + 20
+ ----------------------------------------------------------------------
2 %i %pi         4 %i %pi     4 %i %pi
- --------         --------     --------
5                5            5           3
(625 %e           - 625 %e        ) (%e         x - 1)
4 %i %pi         2 %i %pi           2 %i %pi           4 %i %pi
--------         --------         - --------         - --------
5                5                  5                  5
+ 1/((- 125 %e         - 125 %e         - 125 %e           - 125 %e
4 %i %pi                      4 %i %pi          2 %i %pi
--------                      --------          --------
5           4                 5                 5
+ 500) (%e         x - 1) ) - (- 1544 %e         - 1880 %e
2 %i %pi           4 %i %pi
- --------         - --------
5                  5
- 32 %e           - 368 %e           - 956)
4 %i %pi          2 %i %pi            2 %i %pi            4 %i %pi     2 %i %pi
--------          --------          - --------          - --------     --------
5                 5                   5                   5            5
/((- 4375 %e         - 6875 %e         + 6875 %e           + 4375 %e          ) (%e         x - 1))
4 %i %pi         2 %i %pi          2 %i %pi          4 %i %pi
--------         --------        - --------        - --------
5                5                 5                 5
+ (42 %e         + 170 %e         + 42 %e           - 54 %e           + 170)
4 %i %pi          2 %i %pi           2 %i %pi            4 %i %pi
--------          --------         - --------          - --------
5                 5                  5                   5
/((- 625 %e         + 1875 %e         - 625 %e           - 2500 %e           + 1875)
2 %i %pi
--------
5           2
(%e         x - 1) )
4 %i %pi       2 %i %pi          2 %i %pi         4 %i %pi
--------       --------        - --------       - --------
5              5                 5                5
- (4 %e         - 4 %e         - 12 %e           + 4 %e           - 12)
4 %i %pi           2 %i %pi           4 %i %pi           2 %i %pi
--------         - --------         - --------           --------
5                  5                  5                  5           3
/((625 %e         - 625 %e           + 625 %e           - 625) (%e         x - 1) )
2 %i %pi           4 %i %pi         2 %i %pi           2 %i %pi           4 %i %pi
- --------           --------         --------         - --------         - --------
5                  5                5                  5                  5
+ %e          /((- 125 %e         - 125 %e         + 500 %e           - 125 %e
2 %i %pi
--------
5           4
- 125) (%e         x - 1) )
4 %i %pi           2 %i %pi             2 %i %pi
--------           --------           - --------
5                  5                    5
- (41824 %e         + 42076 %e         + 42160 %e
4 %i %pi                  4 %i %pi         2 %i %pi            4 %i %pi
- --------                  --------         --------          - --------
5                         5                5                   5
+ 41992 %e           + 42328)/((625 %e         - 625 %e         + 1875 %e           - 1875) (x
4 %i %pi
--------
5
- %e        ))
4 %i %pi          2 %i %pi            2 %i %pi            4 %i %pi
--------          --------          - --------          - --------
5                 5                   5                   5
+ (1114 %e         + 1082 %e         + 1082 %e           + 1114 %e
2 %i %pi           2 %i %pi           4 %i %pi
--------         - --------         - --------
5                  5                  5
+ 1018)/((- 1250 %e         + 625 %e           + 625 %e          )
4 %i %pi
--------
5     2
(x - %e        ) )
4 %i %pi        2 %i %pi          2 %i %pi          4 %i %pi
--------        --------        - --------        - --------
5               5                 5                 5
20 %e         + 20 %e         + 20 %e           + 12 %e           + 28
- ----------------------------------------------------------------------
2 %i %pi         4 %i %pi         4 %i %pi
- --------         --------         --------
5                5                5     3
(625 %e           - 625 %e        ) (x - %e        )
4 %i %pi           4 %i %pi         2 %i %pi           2 %i %pi           4 %i %pi
- --------           --------         --------         - --------         - --------
5                  5                5                  5                  5
+ %e          /((- 125 %e         - 125 %e         - 125 %e           - 125 %e
4 %i %pi
--------
5     4
+ 500) (x - %e        ) )
4 %i %pi         2 %i %pi            2 %i %pi           4 %i %pi
--------         --------          - --------         - --------
5                5                   5                  5
- (32 %e         + 956 %e         + 1544 %e           + 368 %e
4 %i %pi          2 %i %pi            2 %i %pi            4 %i %pi
--------          --------          - --------          - --------
5                 5                   5                   5
+ 1880)/((- 4375 %e         - 6875 %e         + 6875 %e           + 4375 %e          ) (x
2 %i %pi
--------
5
- %e        ))
4 %i %pi        2 %i %pi          2 %i %pi           4 %i %pi
--------        --------        - --------         - --------
5               5                 5                  5
+ (170 %e         + 42 %e         + 42 %e           + 170 %e           - 54)
4 %i %pi          2 %i %pi           2 %i %pi            4 %i %pi
--------          --------         - --------          - --------
5                 5                  5                   5
/((- 625 %e         + 1875 %e         - 625 %e           - 2500 %e           + 1875)
2 %i %pi
--------
5     2
(x - %e        ) )
4 %i %pi        2 %i %pi         2 %i %pi         4 %i %pi
--------        --------       - --------       - --------
5               5                5                5
- (- 4 %e         + 12 %e         + 4 %e           - 4 %e           + 12)
4 %i %pi           2 %i %pi           4 %i %pi               2 %i %pi
--------         - --------         - --------               --------
5                  5                  5                      5     3
/((625 %e         - 625 %e           + 625 %e           - 625) (x - %e        ) )
4 %i %pi           4 %i %pi         2 %i %pi           2 %i %pi           4 %i %pi
- --------           --------         --------         - --------         - --------
5                  5                5                  5                  5
+ %e          /((- 125 %e         - 125 %e         + 500 %e           - 125 %e
2 %i %pi
--------
5     4
- 125) (x - %e        ) )
4 %i %pi         2 %i %pi           2 %i %pi          4 %i %pi
--------         --------         - --------        - --------
5                5                  5                 5
120 %e         + 120 %e         - 132 %e           + 36 %e           + 36
- -------------------------------------------------------------------------
4 %i %pi         2 %i %pi            2 %i %pi
--------         --------          - --------
5                5                   5
(625 %e         + 625 %e         - 1250 %e          ) (x - 1)
4 %i %pi        2 %i %pi          2 %i %pi         4 %i %pi
--------        --------        - --------       - --------
5               5                 5                5
36 %e         + 36 %e         - 60 %e           + 4 %e           + 4
+ --------------------------------------------------------------------
4 %i %pi         2 %i %pi            2 %i %pi
--------         --------          - --------
5                5                   5             2
(625 %e         + 625 %e         - 1250 %e          ) (x - 1)
4 %i %pi          4 %i %pi         2 %i %pi           2 %i %pi           4 %i %pi
--------          --------         --------         - --------         - --------
5                 5                5                  5                  5
- (8 %e        )/((500 %e         - 125 %e         - 125 %e           - 125 %e
4 %i %pi
--------
3         5
- 125) (x - 1) ) + %e
4 %i %pi         2 %i %pi           2 %i %pi           4 %i %pi
--------         --------         - --------         - --------
5                5                  5                  5
/((500 %e         - 125 %e         - 125 %e           - 125 %e           - 125)
4
(x - 1) )
(%i4) tex(O);
$${{41992\,e^{{{4\,i\,\pi}\over{5}}}+42160\,e^{{{2\,i\,\pi}\over{5}}} +42076\,e^ {- {{2\,i\,\pi}\over{5}} }+41824\,e^ {- {{4\,i\,\pi }\over{5}} }+42328}\over{\left(625\,e^{{{4\,i\,\pi}\over{5}}}-625\,e ^{{{2\,i\,\pi}\over{5}}}+1875\,e^ {- {{4\,i\,\pi}\over{5}} }-1875 \right)\,\left(e^{{{4\,i\,\pi}\over{5}}}\,x-1\right)}}+{{1082\,e^{{{ 4\,i\,\pi}\over{5}}}+1018\,e^{{{2\,i\,\pi}\over{5}}}+1114\,e^ {- {{2 \,i\,\pi}\over{5}} }+1114\,e^ {- {{4\,i\,\pi}\over{5}} }+1082}\over{ \left(-1250\,e^{{{2\,i\,\pi}\over{5}}}+625\,e^ {- {{2\,i\,\pi}\over{ 5}} }+625\,e^ {- {{4\,i\,\pi}\over{5}} }\right)\,\left(e^{{{4\,i\, \pi}\over{5}}}\,x-1\right)^2}}+{{28\,e^{{{4\,i\,\pi}\over{5}}}+20\,e ^{{{2\,i\,\pi}\over{5}}}+12\,e^ {- {{2\,i\,\pi}\over{5}} }+20\,e ^ {- {{4\,i\,\pi}\over{5}} }+20}\over{\left(625\,e^ {- {{2\,i\,\pi }\over{5}} }-625\,e^{{{4\,i\,\pi}\over{5}}}\right)\,\left(e^{{{4\,i \,\pi}\over{5}}}\,x-1\right)^3}}+{{1}\over{\left(-125\,e^{{{4\,i\, \pi}\over{5}}}-125\,e^{{{2\,i\,\pi}\over{5}}}-125\,e^ {- {{2\,i\,\pi }\over{5}} }-125\,e^ {- {{4\,i\,\pi}\over{5}} }+500\right)\,\left(e ^{{{4\,i\,\pi}\over{5}}}\,x-1\right)^4}}-{{-1544\,e^{{{4\,i\,\pi }\over{5}}}-1880\,e^{{{2\,i\,\pi}\over{5}}}-32\,e^ {- {{2\,i\,\pi }\over{5}} }-368\,e^ {- {{4\,i\,\pi}\over{5}} }-956}\over{\left(- 4375\,e^{{{4\,i\,\pi}\over{5}}}-6875\,e^{{{2\,i\,\pi}\over{5}}}+6875 \,e^ {- {{2\,i\,\pi}\over{5}} }+4375\,e^ {- {{4\,i\,\pi}\over{5}} } \right)\,\left(e^{{{2\,i\,\pi}\over{5}}}\,x-1\right)}}+{{42\,e^{{{4 \,i\,\pi}\over{5}}}+170\,e^{{{2\,i\,\pi}\over{5}}}+42\,e^ {- {{2\,i \,\pi}\over{5}} }-54\,e^ {- {{4\,i\,\pi}\over{5}} }+170}\over{\left( -625\,e^{{{4\,i\,\pi}\over{5}}}+1875\,e^{{{2\,i\,\pi}\over{5}}}-625 \,e^ {- {{2\,i\,\pi}\over{5}} }-2500\,e^ {- {{4\,i\,\pi}\over{5}} }+ 1875\right)\,\left(e^{{{2\,i\,\pi}\over{5}}}\,x-1\right)^2}}-{{4\,e ^{{{4\,i\,\pi}\over{5}}}-4\,e^{{{2\,i\,\pi}\over{5}}}-12\,e^ {- {{2 \,i\,\pi}\over{5}} }+4\,e^ {- {{4\,i\,\pi}\over{5}} }-12}\over{ \left(625\,e^{{{4\,i\,\pi}\over{5}}}-625\,e^ {- {{2\,i\,\pi}\over{5 }} }+625\,e^ {- {{4\,i\,\pi}\over{5}} }-625\right)\,\left(e^{{{2\,i \,\pi}\over{5}}}\,x-1\right)^3}}+{{e^ {- {{2\,i\,\pi}\over{5}} } }\over{\left(-125\,e^{{{4\,i\,\pi}\over{5}}}-125\,e^{{{2\,i\,\pi }\over{5}}}+500\,e^ {- {{2\,i\,\pi}\over{5}} }-125\,e^ {- {{4\,i\, \pi}\over{5}} }-125\right)\,\left(e^{{{2\,i\,\pi}\over{5}}}\,x-1 \right)^4}}-{{41824\,e^{{{4\,i\,\pi}\over{5}}}+42076\,e^{{{2\,i\,\pi }\over{5}}}+42160\,e^ {- {{2\,i\,\pi}\over{5}} }+41992\,e^ {- {{4\,i \,\pi}\over{5}} }+42328}\over{\left(625\,e^{{{4\,i\,\pi}\over{5}}}- 625\,e^{{{2\,i\,\pi}\over{5}}}+1875\,e^ {- {{4\,i\,\pi}\over{5}} }- 1875\right)\,\left(x-e^{{{4\,i\,\pi}\over{5}}}\right)}}+{{1114\,e^{ {{4\,i\,\pi}\over{5}}}+1082\,e^{{{2\,i\,\pi}\over{5}}}+1082\,e^ {- {{2\,i\,\pi}\over{5}} }+1114\,e^ {- {{4\,i\,\pi}\over{5}} }+1018 }\over{\left(-1250\,e^{{{2\,i\,\pi}\over{5}}}+625\,e^ {- {{2\,i\,\pi }\over{5}} }+625\,e^ {- {{4\,i\,\pi}\over{5}} }\right)\,\left(x-e^{ {{4\,i\,\pi}\over{5}}}\right)^2}}-{{20\,e^{{{4\,i\,\pi}\over{5}}}+20 \,e^{{{2\,i\,\pi}\over{5}}}+20\,e^ {- {{2\,i\,\pi}\over{5}} }+12\,e ^ {- {{4\,i\,\pi}\over{5}} }+28}\over{\left(625\,e^ {- {{2\,i\,\pi }\over{5}} }-625\,e^{{{4\,i\,\pi}\over{5}}}\right)\,\left(x-e^{{{4\, i\,\pi}\over{5}}}\right)^3}}+{{e^ {- {{4\,i\,\pi}\over{5}} }}\over{ \left(-125\,e^{{{4\,i\,\pi}\over{5}}}-125\,e^{{{2\,i\,\pi}\over{5}}} -125\,e^ {- {{2\,i\,\pi}\over{5}} }-125\,e^ {- {{4\,i\,\pi}\over{5}} }+500\right)\,\left(x-e^{{{4\,i\,\pi}\over{5}}}\right)^4}}-{{32\,e ^{{{4\,i\,\pi}\over{5}}}+956\,e^{{{2\,i\,\pi}\over{5}}}+1544\,e^ {- {{2\,i\,\pi}\over{5}} }+368\,e^ {- {{4\,i\,\pi}\over{5}} }+1880 }\over{\left(-4375\,e^{{{4\,i\,\pi}\over{5}}}-6875\,e^{{{2\,i\,\pi }\over{5}}}+6875\,e^ {- {{2\,i\,\pi}\over{5}} }+4375\,e^ {- {{4\,i\, \pi}\over{5}} }\right)\,\left(x-e^{{{2\,i\,\pi}\over{5}}}\right)}}+ {{170\,e^{{{4\,i\,\pi}\over{5}}}+42\,e^{{{2\,i\,\pi}\over{5}}}+42\,e ^ {- {{2\,i\,\pi}\over{5}} }+170\,e^ {- {{4\,i\,\pi}\over{5}} }-54 }\over{\left(-625\,e^{{{4\,i\,\pi}\over{5}}}+1875\,e^{{{2\,i\,\pi }\over{5}}}-625\,e^ {- {{2\,i\,\pi}\over{5}} }-2500\,e^ {- {{4\,i\, \pi}\over{5}} }+1875\right)\,\left(x-e^{{{2\,i\,\pi}\over{5}}} \right)^2}}-{{-4\,e^{{{4\,i\,\pi}\over{5}}}+12\,e^{{{2\,i\,\pi }\over{5}}}+4\,e^ {- {{2\,i\,\pi}\over{5}} }-4\,e^ {- {{4\,i\,\pi }\over{5}} }+12}\over{\left(625\,e^{{{4\,i\,\pi}\over{5}}}-625\,e ^ {- {{2\,i\,\pi}\over{5}} }+625\,e^ {- {{4\,i\,\pi}\over{5}} }-625 \right)\,\left(x-e^{{{2\,i\,\pi}\over{5}}}\right)^3}}+{{e^ {- {{4\,i \,\pi}\over{5}} }}\over{\left(-125\,e^{{{4\,i\,\pi}\over{5}}}-125\,e ^{{{2\,i\,\pi}\over{5}}}+500\,e^ {- {{2\,i\,\pi}\over{5}} }-125\,e ^ {- {{4\,i\,\pi}\over{5}} }-125\right)\,\left(x-e^{{{2\,i\,\pi }\over{5}}}\right)^4}}-{{120\,e^{{{4\,i\,\pi}\over{5}}}+120\,e^{{{2 \,i\,\pi}\over{5}}}-132\,e^ {- {{2\,i\,\pi}\over{5}} }+36\,e^ {- {{4 \,i\,\pi}\over{5}} }+36}\over{\left(625\,e^{{{4\,i\,\pi}\over{5}}}+ 625\,e^{{{2\,i\,\pi}\over{5}}}-1250\,e^ {- {{2\,i\,\pi}\over{5}} } \right)\,\left(x-1\right)}}+{{36\,e^{{{4\,i\,\pi}\over{5}}}+36\,e^{ {{2\,i\,\pi}\over{5}}}-60\,e^ {- {{2\,i\,\pi}\over{5}} }+4\,e^ {- {{ 4\,i\,\pi}\over{5}} }+4}\over{\left(625\,e^{{{4\,i\,\pi}\over{5}}}+ 625\,e^{{{2\,i\,\pi}\over{5}}}-1250\,e^ {- {{2\,i\,\pi}\over{5}} } \right)\,\left(x-1\right)^2}}-{{8\,e^{{{4\,i\,\pi}\over{5}}}}\over{ \left(500\,e^{{{4\,i\,\pi}\over{5}}}-125\,e^{{{2\,i\,\pi}\over{5}}}- 125\,e^ {- {{2\,i\,\pi}\over{5}} }-125\,e^ {- {{4\,i\,\pi}\over{5}} }-125\right)\,\left(x-1\right)^3}}+{{e^{{{4\,i\,\pi}\over{5}}} }\over{\left(500\,e^{{{4\,i\,\pi}\over{5}}}-125\,e^{{{2\,i\,\pi }\over{5}}}-125\,e^ {- {{2\,i\,\pi}\over{5}} }-125\,e^ {- {{4\,i\, \pi}\over{5}} }-125\right)\,\left(x-1\right)^4}}$$
(%o4)                                false
(%i5) 
Run Example
rat(0.1234);

rat: replaced 0.1234 by 617/5000 = 0.1234
617
(%o1)/R/                             ----
5000
(%i2) rat(0.12345);

rat: replaced 0.12345 by 2469/20000 = 0.12345
2469
(%o2)/R/                             -----
20000
(%i3) rat(0.12345);

rat: replaced 0.12345 by 2469/20000 = 0.12345
2469
(%o3)/R/                             -----
20000
(%i4) mod(12345, 1000)/100000, numer;
(%o4)                               0.00345
(%i5) lastdigits(fnum, lastn):=block([m:10*fnum, ans, n:lastn], /* it doesn't help when lastn is bigger than the total digits in fnum it returns the whole digits in fnum anyway without erroring! and fnum=%pi stuff works only upto 8 digits cause num(rat(fnum)) has somuch only! */ratprint:false, k:rat(fnum), ans:mod(m, (10^-n))/(mod(m, 10)*denom(k)), return(float(ans)));
(%o5) lastdigits(fnum, lastn) := block([m : 10 fnum, ans, n : lastn],
- n
mod(m, 10   )
ratprint : false, k : rat(fnum), ans : -------------------, return(float(ans)))
mod(m, 10) denom(k)
(%i6) lastdigits(0.12345, 3);
(%o6)                        2.0251113811259619E-8
(%i7) 

Help for Denom