>> printRecursiveSeries(x_{n+1}==1/x_n+2/(3*n),x_1=2/3,10,\n,linenumber)
[1]     2|3
[2]     5|6
[3]     11|30
[4]     223|990
[5]     18398|110385
[6]     54156353|406172646
[7]     814697377619261|7332276398573346
[8]     1327463634199400965148971292737|13938368159093710134064198573714
[9]     9251338425639875332316232138713556382611648237643023083657615|111016061107678503987794785664562676591339778851716277003891308
[10]    684698101325767096988344365704864935802520824311879253005505738143309983824829952722521167450496083751813058245984364340289|9243424367897855809342648937015676633334031128210369915574327464934684781635204361754035760581697130649476286320788918593780

第二项应该是 13/6

>> 1/(2/3)+2/(3*1)
in> 1/(2/3)+2/(3*1)

out> 13|6

------------------------

这里计算的是

\[
\begin{aligned}
x_2=\frac{1}{2\cdot 3}+\frac{2}{3\cdot 1}=\frac{5}{6}\\
x_3=\frac{1}{5\cdot 6}+\frac{2}{3\cdot 2}=\frac{11}{30}\\
\end{aligned}
\]

也即是在替代 x_n 时,  1/x_n 直接替换为 1/2/3 而不是 1/(2/3).  已经解决.

>> :version

Version: 0.601

>> solve(x^2-6x+34==0)

这是一个一元二次方程.

  x^2-6x^1+34 == 0

solution>
        x1 = (6+1*-1^0*2^1*5^1*sqrt(1*-1))|2
        x2 = (6-(1*-1^0*2^1*5^1*sqrt(1*-1)))|2

------------------------

已解决.   2024-5-29

>> solve(x^2+3/2x-2==0)

这是一个一元二次方程.

  x^2+3|2x^1-2 == 0

solution>
        x1 = -3|4+sqrt(41)|2/2
        x2 = -3|4-sqrt(41)|2/2

------------------------

>> :version

Version: 0.601

>> A=[x-3 -5;
A=[x-3 -5;
5 x-3]
A=[x-3 -5;
input> [x-3,-5;5,x-3]
--------------------

x-3     -5
5       x-3

--------------------
>> det(A)
x*x+22*x-3*x-66

分析原因

det(A)= x-3 * x-3-(-5)*5 =x-3*x+22

这里计算的是 (x-3)*(x+22)=x*x+22*x-3*x-66

问题在于 fr_multiplication() and fr_subtraction() 两个函数.

现已修复.

>> lim((3x^5-1)/(2.5x^5+1),x,inf)
result> 96|3125

------------------------

这里程序将 2.5x^5识别为  2.5^5 x^5  

>> 2.5^5
in> 2.5^5

out> 97.65625
------------------------

>> 3/97.65625
in> 3/97.65625

out> 0.03072
------------------------

>> :mode fraction
Switch into fraction calculating mode.
e.g., 1/2+1/3 will return 5/6

>> 3/97.65625
in> 3/97.65625

out> 96|3125

------------------------

当系数是小数时, 在系数和x之间加上*, 可以避免上面的问题.

>> lim((3x^5-1)/(2.5*x^5+1),x,inf)
result> 6|5

------------------------

>> :version

Version: 0.597

>> :mode polyn
Switch into polynomial mode.

>> symbol(a,b,c,d)
out> a is a variable for polynomial.
out> b is a variable for polynomial.
out> c is a variable for polynomial.
out> d is a variable for polynomial.

------------------------

>> (a+b)(c+d)
in> (a+b)*(c+d)

out> ac+2ad+bc
------------------------

这里正确答案应该是 ac+ad+bc+bd

 v607已经解决. 

>> :mode polyn
Switch into polynomial mode.

>> symbol(x,y)
out> x is a variable for polynomial.
out> y is a variable for polynomial.

------------------------

>> (x+y)(x-y)
in> (x+y)*(x-y)

out> +1x^2-1xy+1xy-1y^2
------------------------

>> (x+y)(x-y)+0
in> (x+y)*(x-y)+0

out> +1x^2+0-1y^2+0
------------------------

>> (x^2+xy+y^2)(x-y)
in> (x^2+xy+y^2)*(x-y)

out> +1x^3-1x^2y+1x^2y+0x^y^-1y^3
------------------------

>> (x^2+xy+y^2)(x-y)+0
in> (x^2+xy+y^2)*(x-y)+0

out> +1x^3+0-1y^3
------------------------

>>

海伦公式 (见(1 封私信) 怎么优雅的计算出这个海伦公式？ - 知乎 (zhihu.com))

>> symbol(a,b,c)
out> a is a variable for polynomial.
out> b is a variable for polynomial.
out> c is a variable for polynomial.

------------------------

>> (a+b+c)(a+b-c)(a-b+c)(-a+b+c)
in> (a+b+c)*(a+b-c)*(a-b+c)*(-a+b+c)

out> -a^4+2a^2b^2+0a^b^c^+2a^2c^2+0a^b^+0a^b^c^+0a^b^c^+0a^b^c^+0a^b^c^+0a^b^c^-b^4+2b^2c^2+0a^c^+0b^c^-c^4
------------------------

>>

只需测试

>> ab+ca-ac

 v608已经解决. 

>> (ax^5+bx^4)(px^4+qx^3)
in> (ax^5+bx^4)*(px^4+qx^3)

out> a*a*a*a*a*p*p*p*px^9+(a*a*a*a*a*q*q*q+b*b*b*b*p*p*p*p)x^8+b*b*b*b*q*q*qx^7
------------------------

>> (a(x^5)+b(x^4))(p(x^4)+q(x^3))
in> (a(x^5)+b(x^4))*(p(x^4)+q(x^3))

out> x^7+qx^4
------------------------

>> (a*(x^5)+b*(x^4))(p*(x^4)+q*(x^3))
in> (a*(x^5)+b*(x^4))*(p*(x^4)+q*(x^3))

out> a*px^9+(a*q+b*p)x^8+b*qx^7
------------------------

>> :mode polyn
Switch into polynomial mode.

>> (1.2x)^(1+2)
in> (1.2x)^(1+2)

out> 1.2x^3|1
------------------------

目前改进

>> :mode polyn
Switch into polynomial mode.

>> 1.2x^1.2-x^1
in> 1.2x^1.2-x^1

out> +1.2x^1.2-1x
------------------------

>> 1.2x^1.2-x^1.2
in> 1.2x^1.2-x^1.2

out> +0.2x^1.2
------------------------

Sowya, version 0.59

>> 2+1/(1+1/(0+1/(-1)))

返回 Inf+2,  应返回 Inf

>> 106|5x^3+21|2x^2-101|23x-207|20
in> 106|5x^3+21|2x^2-101|23x-207|20

out> 106|5x^3+21|2x^2-87826087|20000000x^1-207|20
------------------------

SowyaApp.exe  

-------------------

version: v0.589

A=[1,1/2;-3.2,4]

1

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