Using Maple to solve equation 2ab+2bc+2cd+2de-e^2=-578061304296 2ac+2bd+2ce-2de-a^2=-1998272010782 -2ab+2ad+2be-2ce-d^2=-1194036100249 -2ac+2ae-2be-2cd-b^2=-1033536225483 2ad+2ae+2bc+2bd+c^2=3075230855865 There seems to be an integer solution

Using Maple to solve equation 2ab+2bc+2cd+2de-e^2=-578061304296 2ac+2bd+2ce-2de-a^2=-1998272010782 -2ab+2ad+2be-2ce-d^2=-1194036100249 -2ac+2ae-2be-2cd-b^2=-1033536225483 2ad+2ae+2bc+2bd+c^2=3075230855865 There seems to be an integer solution

> evalf(solve({-2*a*b+2*a*d+2*b*e-2*c*e-d^2 = -1194036100249,2*a*b+2*b*c+2*c*d+2*d*e-e^2 = -578061304296,-2*a*c+2*a*e-2*b*e-2*c*d-b^2 = -1033536225483,2*a*c+2*b*d+2*c*e-2*d*e-a^2 = -1998272010782,2*a*...

Maple solves an equation, such as 1 + 3x = B, B takes 12, 3, 4, and so on. How to batch calculate

For example, solve the equation 1 + X / 3 = B
> solve(1+x/3 = b,x);
3b-3
> seq(3*b-3,b = 1 ..100);
0,3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99,102,105,108,111,114,117,120,123,126,129,132,135,138,141,144,147,150,153,156,159,162,165,168,171,174,177,180,183,186,189,192,195,198,201,204,207,210,213,216,219,222,225,228,231,234,237,240,243,246,249,252,255,258,261,264,267,270,273,276,279,282,285, 288,291,294,297

(1) Give an example of a finite group whose elements are in the complex field. (2) give an example of a finite group whose elements are matrices
(1) Give an example of a finite group whose elements are in the complex field
(2) Give an example of a finite group whose elements are matrices
(3) Give an example of an infinite group
To prove this, take three examples~

1. The multiplication of {1, - 1, I, - I} logarithm constitutes a group
2. {[10; 0 1], [10; 0 - 1]} multiplication of matrices
3. Integer set, logarithm addition
The proof is very simple, the combination law is established, only need to verify that the operation is closed, there are unit elements and inverse elements

If C belongs to C (complex field) such that the determinant deta (c) of numerical matrix A (c) = 0, then a (x) is irreversible

To the contrary, if a (λ) is invertible, then there exists a matrix B (λ) such that a (λ) B (λ) = E
Let λ = C have a (c) B (c) = e, then det (a (c)) det (b (c)) = 1
DET (a (c)) ≠ 0, contradiction