比较两个符号表达式

如何解决比较两个符号表达式

我有两个符号表达式 a 和 b，每个表达式都由具有基本算术和小的正整数幂的多项式组成。

simplify(a - b) 不会达到 0，我唯一的选择是 subs 一些随机数到变量中并进行比较。

我会期望像扩展表达式直到没有括号。然后，将所有分数加到一个分数中。

我将数据转换成一个函数，可以调用为：

x = sym('x',[1 8],'real')';
err = func( x ) % should be simplified to zeros

x0 = rand( size(x) )
double( subs(err,x,x0) )

simplify(err)

功能

function err_Dpsi_Dpsi2 = func(in1)
%FUNC
%    ERR_DPSI_DPSI2 = FUNC(IN1)

%    This function was generated by the Symbolic Math Toolbox version 8.4.
%    29-Dec-2020 20:03:34

x1 = in1(1,:);
x2 = in1(2,:);
x3 = in1(3,:);
x4 = in1(4,:);
x5 = in1(5,:);
x6 = in1(6,:);
x7 = in1(7,:);
x8 = in1(8,:);
t2 = x1.*x6;
t3 = x2.*x5;
t4 = x1.*x7;
t5 = x3.*x5;
t6 = x2.*x7;
t7 = x3.*x6;
t8 = -x2;
t9 = -x3;
t10 = -x6;
t11 = -x7;
t15 = x1./2.0;
t16 = x2./2.0;
t17 = x1./4.0;
t18 = x3./2.0;
t19 = x2./4.0;
t20 = x3./4.0;
t21 = x5./2.0;
t22 = x6./2.0;
t23 = x5./4.0;
t24 = x7./2.0;
t25 = x6./4.0;
t26 = x7./4.0;
t43 = x2.*7.072e+3;
t44 = x3.*7.072e+3;
t45 = x4.*7.071e+3;
t46 = x6.*7.072e+3;
t47 = x7.*7.072e+3;
t48 = x8.*7.071e+3;
t60 = x2.*x8.*-7.071e+3;
t62 = x4.*x7.*-7.071e+3;
t69 = x1.*9.999907193999999e-1;
t70 = x5.*9.999907193999999e-1;
t71 = x1.*1.0000660704;
t72 = x5.*1.0000660704;
t74 = x2.*1.0001321408;
t75 = x3.*1.0001321408;
t76 = x6.*1.0001321408;
t77 = x7.*1.0001321408;
t78 = x1.*1.0000660704;
t79 = x2.*5.000660704e-1;
t80 = x2.*1.0001321408;
t81 = x3.*5.000660704e-1;
t82 = x3.*1.0001321408;
t83 = x5.*1.0000660704;
t84 = x6.*5.000660704e-1;
t85 = x6.*1.0001321408;
t86 = x7.*5.000660704e-1;
t87 = x7.*1.0001321408;
t102 = x1.*9.999907194000001e-1;
t103 = x5.*9.999907194000001e-1;
t104 = x4.*4.999953597e-1;
t105 = x8.*4.999953597e-1;
t108 = x2.*1.000132149530596;
t109 = x3.*1.000132149530596;
t110 = x6.*1.000132149530596;
t111 = x7.*1.000132149530596;
t112 = x2.*1.000056789186827;
t113 = x3.*1.000056789186827;
t114 = x6.*1.000056789186827;
t115 = x7.*1.000056789186827;
t124 = x4.*1.000056789186827;
t125 = x8.*1.000056789186827;
t126 = x4.*9.999814388861295e-1;
t127 = x8.*9.999814388861295e-1;
t128 = x2.*1.000132149530596;
t129 = x3.*1.000132149530596;
t130 = x6.*1.000132149530596;
t131 = x7.*1.000132149530596;
t139 = x4.*2.500307147434136e-1;
t140 = x8.*2.500307147434136e-1;
t141 = x2.*1.000056789186827;
t142 = x3.*1.000056789186827;
t144 = x4.*1.000056789186827;
t145 = x6.*1.000056789186827;
t146 = x7.*1.000056789186827;
t148 = x8.*1.000056789186827;
t157 = x2.*x8.*(-2.500307147434136e-1);
t158 = x4.*x7.*(-2.500307147434136e-1);
t159 = x4.*9.999814388861297e-1;
t160 = x8.*9.999814388861297e-1;
t12 = -t3;
t13 = -t4;
t14 = -t7;
t27 = t2./4.0;
t28 = t3./4.0;
t29 = t4./4.0;
t30 = t5./4.0;
t31 = t6./4.0;
t32 = t7./4.0;
t33 = t8+x1;
t34 = t9+x1;
t35 = t10+x5;
t36 = t11+x5;
t37 = -t16;
t38 = -t18;
t39 = -t20;
t40 = -t22;
t41 = -t24;
t42 = -t26;
t52 = t6.*7.072e+3;
t53 = t48.*x2;
t54 = t7.*7.072e+3;
t55 = t45.*x6;
t56 = t48.*x3;
t57 = t45.*x7;
t58 = -t45;
t59 = -t48;
t88 = -t74;
t89 = -t75;
t90 = -t76;
t91 = -t77;
t92 = -t80;
t93 = -t79;
t94 = -t82;
t95 = -t81;
t96 = -t85;
t97 = -t84;
t98 = -t87;
t99 = -t86;
t116 = -t108;
t117 = -t109;
t118 = -t110;
t119 = -t111;
t120 = -t112;
t121 = -t113;
t122 = -t114;
t123 = -t115;
t132 = -t128;
t133 = -t129;
t134 = -t130;
t135 = -t131;
t136 = t6.*2.500660747652978e-1;
t137 = t7.*2.500660747652978e-1;
t143 = -t139;
t147 = -t140;
t149 = t140.*x2;
t150 = t139.*x6;
t151 = t140.*x3;
t152 = t139.*x7;
t153 = -t141;
t154 = -t142;
t155 = -t145;
t156 = -t146;
t49 = -t28;
t50 = -t29;
t51 = -t32;
t61 = -t54;
t63 = t43+t58;
t64 = t44+t58;
t65 = t46+t59;
t66 = t47+t59;
t67 = t2+t5+t6+t12+t13+t14;
t138 = -t137;
t161 = t15+t38+t93+t104;
t162 = t15+t37+t95+t104;
t163 = t21+t41+t97+t105;
t164 = t21+t40+t99+t105;
t169 = t71+t89+t116+t124;
t170 = t71+t88+t117+t124;
t171 = t72+t91+t118+t125;
t172 = t72+t90+t119+t125;
t173 = t78+t92+t133+t144;
t174 = t78+t94+t132+t144;
t175 = t83+t96+t135+t148;
t176 = t83+t98+t134+t148;
t177 = t69+t120+t121+t126;
t178 = t70+t122+t123+t127;
t179 = t102+t153+t154+t159;
t180 = t103+t155+t156+t160;
t68 = 1.0./t67;
t73 = t27+t30+t31+t49+t50+t51;
t106 = t52+t55+t56+t60+t61+t62;
t165 = t161.^2;
t166 = t162.^2;
t167 = t163.^2;
t168 = t164.^2;
t182 = t136+t138+t150+t151+t157+t158;
t100 = 1.0./t73;
t107 = 1.0./t106;
t181 = t165+t166+t167+t168;
t183 = 1.0./t182;
t101 = t100.^2;
t184 = t183.^2;
err_Dpsi_Dpsi2 = [t181.*(t35.*t68.*t100-t36.*t68.*t100)+t101.*t181.*(t25+t42),-t100.*t169+t100.*t174+t169.*t183-t174.*t183-t101.*t181.*(t23+t42)+t181.*t184.*(t140-x7.*2.500660747652978e-1)+t36.*t68.*t100.*t181+t66.*t107.*t181.*t183.*1.0,-t100.*t170+t100.*t173+t170.*t183-t173.*t183-t181.*t184.*(t140-x6.*2.500660747652978e-1)+t101.*t181.*(t23-t25)-t35.*t68.*t100.*t181-t65.*t107.*t181.*t183.*1.0,t100.*t177-t100.*t179-t177.*t183+t179.*t183+t181.*(t65.*t107.*t183.*9.998585972850678e-1-t66.*t107.*t183.*9.998585972850678e-1)-t181.*t184.*(x6.*2.500307147434136e-1-x7.*2.500307147434136e-1),-t181.*(t33.*t68.*t100-t34.*t68.*t100)-t101.*t181.*(t19+t39),-t100.*t171+t100.*t176+t171.*t183-t176.*t183+t101.*t181.*(t17+t39)-t181.*t184.*(t139-x3.*2.500660747652978e-1)-t34.*t68.*t100.*t181-t64.*t107.*t181.*t183.*1.0,-t100.*t172+t100.*t175+t172.*t183-t175.*t183+t181.*t184.*(t139-x2.*2.500660747652978e-1)-t101.*t181.*(t17-t19)+t33.*t68.*t100.*t181+t63.*t107.*t181.*t183.*1.0,t100.*t178-t100.*t180-t178.*t183+t180.*t183-t181.*(t63.*t107.*t183.*9.998585972850678e-1-t64.*t107.*t183.*9.998585972850678e-1)+t181.*t184.*(x2.*2.500307147434136e-1-x3.*2.500307147434136e-1)];

解决方法

我找到了我要找的东西

num = numden( err ) % convert to rational polynomial,and we care only about the numerator
collect( num ) % cancel terms--not needed,numden does some version of simplify

不过，我的例子并不好。出于某种原因，存在精度问题。我认为符号使用了精确的算术，但我没有研究。但是，如果我使用变量而不是有限精度系数，那么它会输出零。