数的运算测试实例.txt

由中科院数学机械化研究所开发的 数学机械化平台（Dos平台运行）能进行各类复杂的数学运算。包括数值运算和多项式运算等。 挺不错的

"数的运算"测试实例
                

数的算术运算（整数，分数，浮点数）：
=================================

>42384023234/23422; //化简
 432490033/239

>iquo(42384023234,23422);
 1809581
>irem(42384023234,23422);
 17052

>2^10000;

混合运算：
>245234523454353123-234534534342342.23423423*34233454354;
- 8028927030610694830750765.84933742

指定浮点数的精度：
>SetPrecision(1.2345678,5); 
 1.23457
>SetPrecision(0.00034234932423,5); 
 0.00034235
>SetPrecision(123.0078924679,5); 
 123.00789
注意：
SetPrecision(f,d)返回一个新的浮点数，它保留f的小数点后d位有效数字。

生成素数表：
===========

>primetable();
该函数返回[1, MAXPRIME]内的所有奇素数的表。
素数表的上界MAXPRIME由程序中的宏指定,通常取上界为65536。
 
生成素数：
=========
 
>primegen(1000000); 
 1000541
>nextprime(1000000); 
 1000003
>prevprime(1000000); 
 999983

>primegen(1234567890);
 1234568827
>nextprime(1234567890);
 1234567891

>primegen(10000000000);  
 10000000793
>nextprime(10000000000);
 10000000019

>primegen(10000000000000000);  
 10000000000004579
>nextprime(10000000000000000);
 10000000000000061

>primegen(7438750237508273048572834750); 
 7438750237508273048572838833
>nextprime(7438750237508273048572834750); 
 7438750237508273048572834799

>nextprime(1000000000); 
 1000000007
>prevprime(1000000000);  
 999999937

注意：
primegen(TBigInt bn); 
生成大于指定数bn的某个指定范围（该范围由程序中的宏指定）内的一个"随机"素数。
该算法通常用于生成大于素数表上界(65536)的素数，因为小于素数表上界的素数可
直接在素数表中得到,即：primegen(bn) > 65536

nextprime(TBigInt bn)：生成指定数bn的下一个素数。
prevprime(TBigInt bn)：生成指定数bn的前一个素数。(bn < 2^32)

素数检验：
========

>isprime(863148947551509220928522167); 
 1 //是素数
>isprime(144927536233); 
 1 //是素数
>isprime(7438750237508273048572839409); 
 1 //是素数
>isprime(4153739648461628337143836935446116357); 
 0 //不是素数

 
素数分解：
========

>ifactor(1000000); 
 [2,6,5,6]

>ifactor(223092870);
 [2,1,3,1,5,1,7,1,11,1,13,1,17,1,19,1,23,1]

>ifactor(29566148020502835);
 [3,1,5,1,7,1,65551,1,65543,1,65539,1]
  
>ifactor(4153739648461628337143836935446116357);
 [5490517,3,158416267,2]

>ifactor(120941505518150933290556893886697069182713526687);
 [1000003,2,11146987,1,2876551,3,455825939,1]
  
>ifactor(348123947210392342302342374);
 [2,1,11909,1,11146987,1,2876551,1,455825939,1]
  
>ifactor(3264123764912374639287462138746882);  
 [2,1,11,1,19,1,83,1,109,1,863148947551509220928522167,1]
  
>ifactor(2048701579966097269575);
 [3,1,5,2,23,3,11909,1,65537,1,2876551,1]

>ifactor(14616046333958937504381949829);
 [1000003,1,11146987,1,2876551,1,455825939,1]

>ifactor(137788442423639097914413);
 [5490517,1,158416267,2]

>ifactor(3475234785728475824500);
 [2,2,5,3,61,1,131,1,5490517,1,158416267,1]
 
最大公因子:
==========

>igcd(59759821449735512944,40967491029104);
 412342768

>a:=67936132211740542899654786013974002719008747564650375881459612567949;
>b:=149317507337279410597748726442677210541619469904891813839581127;
>igcd(a,b);  
 78707310487320487238471208741028734128347


有限域上数的运算：
================

算术运算：
>imod_prod(32423422141412,1234216868762348,53);
 16
>imod_exp(2,1000000000000,53);   
 46

有限域上的平方根：
>imod_sqrt(1,7);
 1
>imod_sqrt(4,5);
 No solution
>imod_sqrt(4,7);
 2
>imod_sqrt(12,13);
 8
>imod_sqrt(3,17);
 No solution

中国剩余定理：
>chrem([3,5,7],[1,2,4]);
 67
>chrem([3,5,7],[1,4,4]); 
 4
>chrem([3,5,7],[1,0,3]); 
 10
>chrem([3,5,7,11],[1,0,2,1]);
 100
>chrem([3,5,7,11,13],[1,0,5,8,3]);
 250
>chrem([5,7,11],[4236342344762197,2342341234234223423,142342314134234]);
 82
注意：chrem(list1,list2)中list1是一个两两互素的整数表，list2是一个整数表。
  
逆元：
>imod_inv(34141234123897857925345234,23); 
 19
>imod_inv(104371083471024712347102834710234324,144927536233);
 59192554942

有限域上数的两种表示：
>imod(341414124124,29);
 25
>imod0(341414124124,29);
 -4

其它函数： 
=========

>ifactorial(1000); //阶乘

数的取整：
>ceil(837401273401834710298472313424.9123414134);
 837401273401834710298472313425

>floor(837401273401834710298472313424.9123414134);
 837401273401834710298472313424

>ceil(18374018273401827340182740217840130/1347120347098347012);
 13639477952343946

>floor(18374018273401827340182740217840130/1347120347098347012);
 13639477952343945

对数，平方根：
>isqrt(834702134701238740283740238740238740234702834702347223);
 913620344947089463775536168
 
>ilog2(234712387401274021384701237401238470123874012384);
 157

>ilog10(234712387401274021384701237401238470123874012384);
 47

随机数生成：
>random(1000); //随机生成十进制1000位的大整数

 


###########多项式的运算

>f1=(73*x^2+3*y^2*z+z^2)^7*((79*u^2-8*v*w+3*u^3+67*v)^2)*(x+y);
f1=(z^2+73*x^2+3*y^2*z)^7*(79*u^2+67*v+-8*v*w+3*u^3)^2*(y+x)
>f2=((68*x^2+3*y^2*z+z^2)*x^3*y^2)*f1*(x-y);
f2=x^3*(z^2+68*x^2+3*y^2*z)*(z^2+73*x^2+3*y^2*z)^7*(79*u^2+67*v+-8*v*w+3*u^3)^2*
(y+x)*(-y+x)
>g1=(73*x^2+3*y^2*z+z^2)*((79*u^2-8*v*w+3*u^3+67*v));
g1=(z^2+73*x^2+3*y^2*z)*(79*u^2+67*v+-8*v*w+3*u^3)
>g2=(73*x^2+3*y^2*z+z^2)*((78*y*z+3*z^3)^3);
g2=(73*x^2+3*y^2*z+z^2)*((78*y*z+3*z^3)^3);
>expand(f1*f2);
68*x^8+68*y*x^7+3*z*y^2*x^6-68*y^2*x^6+z^2*x^6+3*z*y^3*x^5-68*y^3*x^5+z^2*y*x^5-
3*z*y^4*x^4-z^2*y^2*x^4-3*z*y^5*x^3-z^2*y^3*x^3
>coeff(f1,x,2);
3352671*u^6*z^6*y^13+176574006*u^5*z^6*y^13+2324891079*u^4*z^6*y^13-17880912*w*v
*u^3*z^6*y^13+149752638*v*u^3*z^6*y^13-470864016*w*v*u^2*z^6*y^13+3943486134*v*u
^2*z^6*y^13+23841216*w^2*v^2*z^6*y^13-399340368*w*v^2*z^6*y^13+1672237791*v^2*z^
6*y^13+6705342*u^6*z^7*y^11+353148012*u^5*z^7*y^11+4649782158*u^4*z^7*y^11-35761
824*w*v*u^3*z^7*y^11+299505276*v*u^3*z^7*y^11-941728032*w*v*u^2*z^7*y^11+7886972
268*v*u^2*z^7*y^11+47682432*w^2*v^2*z^7*y^11-798680736*w*v^2*z^7*y^11+3344475582
*v^2*z^7*y^11+5587785*u^6*z^8*y^9+294290010*u^5*z^8*y^9+3874818465*u^4*z^8*y^9-2
9801520*w*v*u^3*z^8*y^9+249587730*v*u^3*z^8*y^9-784773360*w*v*u^2*z^8*y^9+657247
6890*v*u^2*z^8*y^9+39735360*w^2*v^2*z^8*y^9-665567280*w*v^2*z^8*y^9+2787062985*v
^2*z^8*y^9+2483460*u^6*z^9*y^7+130795560*u^5*z^9*y^7+1722141540*u^4*z^9*y^7-1324
5120*w*v*u^3*z^9*y^7+110927880*v*u^3*z^9*y^7-348788160*w*v*u^2*z^9*y^7+292110084
0*v*u^2*z^9*y^7+17660160*w^2*v^2*z^9*y^7-295807680*w*v^2*z^9*y^7+1238694660*v^2*
z^9*y^7+620865*u^6*z^10*y^5+32698890*u^5*z^10*y^5+430535385*u^4*z^10*y^5-3311280
*w*v*u^3*z^10*y^5+27731970*v*u^3*z^10*y^5-87197040*w*v*u^2*z^10*y^5+730275210*v*
u^2*z^10*y^5+4415040*w^2*v^2*z^10*y^5-73951920*w*v^2*z^10*y^5+309673665*v^2*z^10
*y^5+82782*u^6*z^11*y^3+4359852*u^5*z^11*y^3+57404718*u^4*z^11*y^3-441504*w*v*u^
3*z^11*y^3+3697596*v*u^3*z^11*y^3-11626272*w*v*u^2*z^11*y^3+97370028*v*u^2*z^11*
y^3+588672*w^2*v^2*z^11*y^3-9860256*w*v^2*z^11*y^3+41289822*v^2*z^11*y^3+4599*u^
6*z^12*y+242214*u^5*z^12*y+3189151*u^4*z^12*y-24528*w*v*u^3*z^12*y+205422*v*u^3*
z^12*y-645904*w*v*u^2*z^12*y+5409446*v*u^2*z^12*y+32704*w^2*v^2*z^12*y-547792*w*
v^2*z^12*y+2293879*v^2*z^12*y
>degree(f1,u);
6
>primitive(g1);
219*u^3*x^2+5767*u^2*x^2-584*w*v*x^2+4891*v*x^2+9*u^3*z*y^2+237*u^2*z*y^2-24*w*v
*z*y^2+201*v*z*y^2+3*u^3*z^2+79*u^2*z^2-8*w*v*z^2+67*v*z^2
>lead_term(g1,[x,y,z]);
219*u^3*x^2+5767*u^2*x^2-584*w*v*x^2+4891*v*x^2
>pprem(f2,f1,z);
0
>get_var_list(g1);
[x,u,v,w,y,z]
>substitute(f1,x,0);
19683*u^6*z^7*y^15+1036638*u^5*z^7*y^15+13649067*u^4*z^7*y^15-104976*w*v*u^3*z^7
*y^15+879174*v*u^3*z^7*y^15-2764368*w*v*u^2*z^7*y^15+23151582*v*u^2*z^7*y^15+139
968*w^2*v^2*z^7*y^15-2344464*w*v^2*z^7*y^15+9817443*v^2*z^7*y^15+45927*u^6*z^8*y
^13+2418822*u^5*z^8*y^13+31847823*u^4*z^8*y^13-244944*w*v*u^3*z^8*y^13+2051406*v
*u^3*z^8*y^13-6450192*w*v*u^2*z^8*y^13+54020358*v*u^2*z^8*y^13+326592*w^2*v^2*z^
8*y^13-5470416*w*v^2*z^8*y^13+22907367*v^2*z^8*y^13+45927*u^6*z^9*y^11+2418822*u
^5*z^9*y^11+31847823*u^4*z^9*y^11-244944*w*v*u^3*z^9*y^11+2051406*v*u^3*z^9*y^11
-6450192*w*v*u^2*z^9*y^11+54020358*v*u^2*z^9*y^11+326592*w^2*v^2*z^9*y^11-547041
6*w*v^2*z^9*y^11+22907367*v^2*z^9*y^11+25515*u^6*z^10*y^9+1343790*u^5*z^10*y^9+1
7693235*u^4*z^10*y^9-136080*w*v*u^3*z^10*y^9+1139670*v*u^3*z^10*y^9-3583440*w*v*
u^2*z^10*y^9+30011310*v*u^2*z^10*y^9+181440*w^2*v^2*z^10*y^9-3039120*w*v^2*z^10*
y^9+12726315*v^2*z^10*y^9+8505*u^6*z^11*y^7+447930*u^5*z^11*y^7+5897745*u^4*z^11
*y^7-45360*w*v*u^3*z^11*y^7+379890*v*u^3*z^11*y^7-1194480*w*v*u^2*z^11*y^7+10003
770*v*u^2*z^11*y^7+60480*w^2*v^2*z^11*y^7-1013040*w*v^2*z^11*y^7+4242105*v^2*z^1
1*y^7+1701*u^6*z^12*y^5+89586*u^5*z^12*y^5+1179549*u^4*z^12*y^5-9072*w*v*u^3*z^1
2*y^5+75978*v*u^3*z^12*y^5-238896*w*v*u^2*z^12*y^5+2000754*v*u^2*z^12*y^5+12096*
w^2*v^2*z^12*y^5-202608*w*v^2*z^12*y^5+848421*v^2*z^12*y^5+189*u^6*z^13*y^3+9954
*u^5*z^13*y^3+131061*u^4*z^13*y^3-1008*w*v*u^3*z^13*y^3+8442*v*u^3*z^13*y^3-2654
4*w*v*u^2*z^13*y^3+222306*v*u^2*z^13*y^3+1344*w^2*v^2*z^13*y^3-22512*w*v^2*z^13*
y^3+94269*v^2*z^13*y^3+9*u^6*z^14*y+474*u^5*z^14*y+6241*u^4*z^14*y-48*w*v*u^3*z^
14*y+402*v*u^3*z^14*y-1264*w*v*u^2*z^14*y+10586*v*u^2*z^14*y+64*w^2*v^2*z^14*y-1
072*w*v^2*z^14*y+4489*v^2*z^14*y
>gcd(g1,g2);
73*x^2+3*z*y^2+z^2
>f1;
(z^2+73*x^2+3*y^2*z)^7*(79*u^2+67*v+-8*v*w+3*u^3)^2*(y+x)
>f2;
x^3*(z^2+68*x^2+3*y^2*z)*(z^2+73*x^2+3*y^2*z)^7*(79*u^2+67*v+-8*v*w+3*u^3)^2*(y+
x)*(-y+x)
>factor(gcd(f1,f2));
[[1],1,[x+y],1,[73*x^2+3*z*y^2+z^2],7,[3*u^3+79*u^2-8*w*v+67*v],2]
>squarefree(f1);
[1,1,x+y,1,73*x^2+3*z*y^2+z^2,7,3*u^3+79*u^2-8*w*v+67*v,2]
>factor(g1);
[[1],1,[73*x^2+3*z*y^2+z^2],1,[3*u^3+79*u^2-8*w*v+67*v],1]
>factor(g2);
[[27],1,[z],3,[26*y+z^2],3,[73*x^2+3*z*y^2+z^2],1]
>gcd(g1,g2);
73*x^2+3*z*y^2+z^2
>pmod_gcd(g1,g2,13);
x^2+2*z*y^2+5*z^2
>pmod_gcd(g1,g2,7);
x^2+z*y^2+5*z^2
>pmod_factor(g1,11);
[u^3*x^2+8*u^2*x^2+w*v*x^2+4*v*x^2+2*u^3*z*y^2+5*u^2*z*y^2+2*w*v*z*y^2+8*v*z*y^2
+8*u^3*z^2+9*u^2*z^2+8*w*v*z^2+10*v*z^2]
>resultant(g1,g2,x);
SR1=[219*u^3*x^2+5767*u^2*x^2-584*w*v*x^2+4891*v*x^2+9*u^3*z*y^2+237*u^2*z*y^2-2
4*w*v*z*y^2+201*v*z*y^2+3*u^3*z^2+79*u^2*z^2-8*w*v*z^2+67*v*z^2,34642296*z^3*y^3
*x^2+3997188*z^5*y^2*x^2+153738*z^7*y*x^2+1971*z^9*x^2+1423656*z^4*y^5+164268*z^
6*y^4+6318*z^8*y^3+474552*z^5*y^3+81*z^10*y^2+54756*z^7*y^2+2106*z^9*y+27*z^11]
0
>derivative(g1,y);
18*u^3*z*y+474*u^2*z*y-48*w*v*z*y+402*v*z*y




>f1=(73*x^2+3*y^2*z+z^2)^7*((79*u^2-8*v*w+3*u^3+67*v)^2)*(x+y);
f1=(z^2+73*x^2+3*y^2*z)^7*(79*u^2+67*v+-8*v*w+3*u^3)^2*(y+x)
>f2=((68*x^2+3*y^2*z+z^2)*x^3*y^2)*f1*(x-y);
f2=x^3*(z^2+68*x^2+3*y^2*z)*(z^2+73*x^2+3*y^2*z)^7*(79*u^2+67*v+-8*v*w+3*u^3)^2*
(y+x)*(-y+x)
>g1=(73*x^2+3*y^2*z+z^2)*((79*u^2-8*v*w+3*u^3+67*v));
g1=(z^2+73*x^2+3*y^2*z)*(79*u^2+67*v+-8*v*w+3*u^3)
>g2=(73*x^2+3*y^2*z+z^2)*((78*y*z+3*z^3)^3);
g2=(73*x^2+3*y^2*z+z^2)*((78*y*z+3*z^3)^3);
>expand(f1*f2);
68*x^8+68*y*x^7+3*z*y^2*x^6-68*y^2*x^6+z^2*x^6+3*z*y^3*x^5-68*y^3*x^5+z^2*y*x^5-
3*z*y^4*x^4-z^2*y^2*x^4-3*z*y^5*x^3-z^2*y^3*x^3
>coeff(f1,x,2);
3352671*u^6*z^6*y^13+176574006*u^5*z^6*y^13+2324891079*u^4*z^6*y^13-17880912*w*v
*u^3*z^6*y^13+149752638*v*u^3*z^6*y^13-470864016*w*v*u^2*z^6*y^13+3943486134*v*u
^2*z^6*y^13+23841216*w^2*v^2*z^6*y^13-399340368*w*v^2*z^6*y^13+1672237791*v^2*z^
6*y^13+6705342*u^6*z^7*y^11+353148012*u^5*z^7*y^11+4649782158*u^4*z^7*y^11-35761
824*w*v*u^3*z^7*y^11+299505276*v*u^3*z^7*y^11-941728032*w*v*u^2*z^7*y^11+7886972
268*v*u^2*z^7*y^11+47682432*w^2*v^2*z^7*y^11-798680736*w*v^2*z^7*y^11+3344475582
*v^2*z^7*y^11+5587785*u^6*z^8*y^9+294290010*u^5*z^8*y^9+3874818465*u^4*z^8*y^9-2
9801520*w*v*u^3*z^8*y^9+249587730*v*u^3*z^8*y^9-784773360*w*v*u^2*z^8*y^9+657247
6890*v*u^2*z^8*y^9+39735360*w^2*v^2*z^8*y^9-665567280*w*v^2*z^8*y^9+2787062985*v
^2*z^8*y^9+2483460*u^6*z^9*y^7+130795560*u^5*z^9*y^7+1722141540*u^4*z^9*y^7-1324
5120*w*v*u^3*z^9*y^7+110927880*v*u^3*z^9*y^7-348788160*w*v*u^2*z^9*y^7+292110084
0*v*u^2*z^9*y^7+17660160*w^2*v^2*z^9*y^7-295807680*w*v^2*z^9*y^7+1238694660*v^2*
z^9*y^7+620865*u^6*z^10*y^5+32698890*u^5*z^10*y^5+430535385*u^4*z^10*y^5-3311280
*w*v*u^3*z^10*y^5+27731970*v*u^3*z^10*y^5-87197040*w*v*u^2*z^10*y^5+730275210*v*
u^2*z^10*y^5+4415040*w^2*v^2*z^10*y^5-73951920*w*v^2*z^10*y^5+309673665*v^2*z^10
*y^5+82782*u^6*z^11*y^3+4359852*u^5*z^11*y^3+57404718*u^4*z^11*y^3-441504*w*v*u^
3*z^11*y^3+3697596*v*u^3*z^11*y^3-11626272*w*v*u^2*z^11*y^3+97370028*v*u^2*z^11*
y^3+588672*w^2*v^2*z^11*y^3-9860256*w*v^2*z^11*y^3+41289822*v^2*z^11*y^3+4599*u^
6*z^12*y+242214*u^5*z^12*y+3189151*u^4*z^12*y-24528*w*v*u^3*z^12*y+205422*v*u^3*
z^12*y-645904*w*v*u^2*z^12*y+5409446*v*u^2*z^12*y+32704*w^2*v^2*z^12*y-547792*w*
v^2*z^12*y+2293879*v^2*z^12*y
>degree(f1,u);
6
>primitive(g1);
219*u^3*x^2+5767*u^2*x^2-584*w*v*x^2+4891*v*x^2+9*u^3*z*y^2+237*u^2*z*y^2-24*w*v
*z*y^2+201*v*z*y^2+3*u^3*z^2+79*u^2*z^2-8*w*v*z^2+67*v*z^2
>lead_term(g1,[x,y,z]);
219*u^3*x^2+5767*u^2*x^2-584*w*v*x^2+4891*v*x^2
>pprem(f2,f1,z);
0
>get_var_list(g1);
[x,u,v,w,y,z]
>substitute(f1,x,0);
19683*u^6*z^7*y^15+1036638*u^5*z^7*y^15+13649067*u^4*z^7*y^15-104976*w*v*u^3*z^7
*y^15+879174*v*u^3*z^7*y^15-2764368*w*v*u^2*z^7*y^15+23151582*v*u^2*z^7*y^15+139
968*w^2*v^2*z^7*y^15-2344464*w*v^2*z^7*y^15+9817443*v^2*z^7*y^15+45927*u^6*z^8*y
^13+2418822*u^5*z^8*y^13+31847823*u^4*z^8*y^13-244944*w*v*u^3*z^8*y^13+2051406*v
*u^3*z^8*y^13-6450192*w*v*u^2*z^8*y^13+54020358*v*u^2*z^8*y^13+326592*w^2*v^2*z^
8*y^13-5470416*w*v^2*z^8*y^13+22907367*v^2*z^8*y^13+45927*u^6*z^9*y^11+2418822*u
^5*z^9*y^11+31847823*u^4*z^9*y^11-244944*w*v*u^3*z^9*y^11+2051406*v*u^3*z^9*y^11
-6450192*w*v*u^2*z^9*y^11+54020358*v*u^2*z^9*y^11+326592*w^2*v^2*z^9*y^11-547041
6*w*v^2*z^9*y^11+22907367*v^2*z^9*y^11+25515*u^6*z^10*y^9+1343790*u^5*z^10*y^9+1
7693235*u^4*z^10*y^9-136080*w*v*u^3*z^10*y^9+1139670*v*u^3*z^10*y^9-3583440*w*v*
u^2*z^10*y^9+30011310*v*u^2*z^10*y^9+181440*w^2*v^2*z^10*y^9-3039120*w*v^2*z^10*
y^9+12726315*v^2*z^10*y^9+8505*u^6*z^11*y^7+447930*u^5*z^11*y^7+5897745*u^4*z^11
*y^7-45360*w*v*u^3*z^11*y^7+379890*v*u^3*z^11*y^7-1194480*w*v*u^2*z^11*y^7+10003
770*v*u^2*z^11*y^7+60480*w^2*v^2*z^11*y^7-1013040*w*v^2*z^11*y^7+4242105*v^2*z^1
1*y^7+1701*u^6*z^12*y^5+89586*u^5*z^12*y^5+1179549*u^4*z^12*y^5-9072*w*v*u^3*z^1
2*y^5+75978*v*u^3*z^12*y^5-238896*w*v*u^2*z^12*y^5+2000754*v*u^2*z^12*y^5+12096*
w^2*v^2*z^12*y^5-202608*w*v^2*z^12*y^5+848421*v^2*z^12*y^5+189*u^6*z^13*y^3+9954
*u^5*z^13*y^3+131061*u^4*z^13*y^3-1008*w*v*u^3*z^13*y^3+8442*v*u^3*z^13*y^3-2654
4*w*v*u^2*z^13*y^3+222306*v*u^2*z^13*y^3+1344*w^2*v^2*z^13*y^3-22512*w*v^2*z^13*
y^3+94269*v^2*z^13*y^3+9*u^6*z^14*y+474*u^5*z^14*y+6241*u^4*z^14*y-48*w*v*u^3*z^
14*y+402*v*u^3*z^14*y-1264*w*v*u^2*z^14*y+10586*v*u^2*z^14*y+64*w^2*v^2*z^14*y-1
072*w*v^2*z^14*y+4489*v^2*z^14*y
>gcd(g1,g2);
73*x^2+3*z*y^2+z^2
>f1;
(z^2+73*x^2+3*y^2*z)^7*(79*u^2+67*v+-8*v*w+3*u^3)^2*(y+x)
>f2;
x^3*(z^2+68*x^2+3*y^2*z)*(z^2+73*x^2+3*y^2*z)^7*(79*u^2+67*v+-8*v*w+3*u^3)^2*(y+
x)*(-y+x)
>factor(gcd(f1,f2));
[[1],1,[x+y],1,[73*x^2+3*z*y^2+z^2],7,[3*u^3+79*u^2-8*w*v+67*v],2]
>squarefree(f1);
[1,1,x+y,1,73*x^2+3*z*y^2+z^2,7,3*u^3+79*u^2-8*w*v+67*v,2]
>factor(g1);
[[1],1,[73*x^2+3*z*y^2+z^2],1,[3*u^3+79*u^2-8*w*v+67*v],1]
>factor(g2);
[[27],1,[z],3,[26*y+z^2],3,[73*x^2+3*z*y^2+z^2],1]
>gcd(g1,g2);
73*x^2+3*z*y^2+z^2
>pmod_gcd(g1,g2,13);
x^2+2*z*y^2+5*z^2
>pmod_gcd(g1,g2,7);
x^2+z*y^2+5*z^2
>pmod_factor(g1,11);
[u^3*x^2+8*u^2*x^2+w*v*x^2+4*v*x^2+2*u^3*z*y^2+5*u^2*z*y^2+2*w*v*z*y^2+8*v*z*y^2
+8*u^3*z^2+9*u^2*z^2+8*w*v*z^2+10*v*z^2]
>resultant(g1,g2,x);
SR1=[219*u^3*x^2+5767*u^2*x^2-584*w*v*x^2+4891*v*x^2+9*u^3*z*y^2+237*u^2*z*y^2-2
4*w*v*z*y^2+201*v*z*y^2+3*u^3*z^2+79*u^2*z^2-8*w*v*z^2+67*v*z^2,34642296*z^3*y^3
*x^2+3997188*z^5*y^2*x^2+153738*z^7*y*x^2+1971*z^9*x^2+1423656*z^4*y^5+164268*z^
6*y^4+6318*z^8*y^3+474552*z^5*y^3+81*z^10*y^2+54756*z^7*y^2+2106*z^9*y+27*z^11]
0
>derivative(g1,y);
18*u^3*z*y+474*u^2*z*y-48*w*v*z*y+402*v*z*y