Calc; Div by 0 in solving system

Calc; Div by 0 in solving system

[Christopher Howard]

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Place this on stack with algebriac mode:

[2 * x - 3 * y + z = 5, x + y - 2 * z = 0, -x + 2 * y + 3 * z = -3]

run command 'a S x,y,z'

Receive error 'Division by zero: 1'

I enabled Debug on Error but could not find the backtrace

Emacs  : GNU Emacs 25.1.1 (x86_64-pc-linux-gnu, GTK+ Version 3.22.11)
 of 2017-09-14, modified by Debian
Package: Calc


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Christopher Howard
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Re: Calc; Div by 0 in solving system

[Eli Zaretskii]

> From: Christopher Howard <christopher.howard@qlfiles.net>
> Date: Sun, 21 Apr 2019 07:37:47 -0800
> 
> Place this on stack with algebriac mode:
> 
> [2 * x - 3 * y + z = 5, x + y - 2 * z = 0, -x + 2 * y + 3 * z = -3]
> 
> run command 'a S x,y,z'
> 
> Receive error 'Division by zero: 1'
> 
> I enabled Debug on Error but could not find the backtrace

Here's the backtrace, obtained by setting debug-on-message to
"Division by zero":

  Debugger entered--Lisp error: "Division by zero: 1."
    message("%s%s" "Division by zero: 1." "")
    calc-explain-why((* "Division by zero" (float 1 0)) nil)
    calc-do-handle-whys()
    calc-handle-whys()
    calc-enter-result(1 "solv" (calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
    #f(compiled-function () #<bytecode 0x2000000001d6b378>)()
    calc-do(#f(compiled-function () #<bytecode 0x2000000001d6b378>) 102)
    calc-solve-for("x,y,z")
    funcall-interactively(calc-solve-for "x,y,z")
    call-interactively(calc-solve-for nil nil)
    command-execute(calc-solve-for)

Re: Calc; Div by 0 in solving system

[Mattias Engdegård]

21 apr. 2019 kl. 17.37 skrev Christopher Howard <christopher.howard@qlfiles.net>:
> 
> Place this on stack with algebriac mode:
> 
> [2 * x - 3 * y + z = 5, x + y - 2 * z = 0, -x + 2 * y + 3 * z = -3]
> 
> run command 'a S x,y,z'
> 
> Receive error 'Division by zero: 1'
> 
> I enabled Debug on Error but could not find the backtrace

This is the backtrace I get in Emacs 26.1:

* math-reject-arg((float 1 0) "*Division by zero")
  math-div-by-zero((float 1 0) 0)
  math-div((float 1 0) 0)
  math-float((frac 1 0))
  math-mul((frac 1 0) (float 138629436111989 -14))
  math-mul-objects-fancy((frac 1 0) (cplx (float 138629436111989 -14) (float 314159265358979 -14)))
  math-mul((frac 1 0) (cplx (float 138629436111989 -14) (float 314159265358979 -14)))
  math-pow-fancy(-4 (frac 1 0))
  math-pow(-4 (frac 1 0))
  math-poly-laguerre-root((4) 0 t)
  math-poly-any-root((4) 0 t)
  math-try-solve-for((+ (+ (- (* 2 (- (var z var-z) (float 1 0))) (/ (- (+ 5 (* 3 (- (var z var-z) (float 1 0)))) (var z var-z)) 2)) (* 3 (var z var-z))) 3) 0 nil nil)
  math-try-solve-for((calcFunc-eq (+ (- (* 2 (- (var z var-z) (float 1 0))) (/ (- (+ 5 (* 3 (- (var z var-z) (float 1 0)))) (var z var-z)) 2)) (* 3 (var z var-z))) -3) 0 nil)
  math-solve-for((calcFunc-eq (+ (- (* 2 (- (var z var-z) (float 1 0))) (/ (- (+ 5 (* 3 (- (var z var-z) (float 1 0)))) (var z var-z)) 2)) (* 3 (var z var-z))) -3) 0 (var z var-z) nil)
  math-solve-system-rec((((calcFunc-eq (+ (- (* 2 (- (var z var-z) (float 1 0))) (/ (- (+ 5 (* 3 (- (var z var-z) (float 1 0)))) (var z var-z)) 2)) (* 3 (var z var-z))) -3))) ((var z var-z)) (((var y var-y) (- (var z var-z) (float 1 0))) ((var x var-x) (/ (- (+ 5 (* 3 (- (var z var-z) (float 1 0)))) (var z var-z)) 2))))
  math-solve-system-rec((((calcFunc-eq (- (+ (/ (- (+ 5 (* 3 (var y var-y))) (var z var-z)) 2) (var y var-y)) (* 2 (var z var-z))) 0)) ((calcFunc-eq (+ (- (* 2 (var y var-y)) (/ (- (+ 5 (* 3 (var y var-y))) (var z var-z)) 2)) (* 3 (var z var-z))) -3))) ((var y var-y) (var z var-z)) (((var x var-x) (/ (- (+ 5 (* 3 (var y var-y))) (var z var-z)) 2))))
  math-solve-system-rec((((calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5)) ((calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0)) ((calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3))) ((var x var-x) (var y var-y) (var z var-z)) nil)
  math-solve-system((vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z)) nil)
  calcFunc-solve((vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z)))
  apply(calcFunc-solve ((vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
  math-normalize((calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
  math-simplify((calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
  calc-normalize-fancy((calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
  calc-normalize((calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
  math-evaluate-expr((calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
  mapcar(math-evaluate-expr ((calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z)))))
  #f(compiled-function () #<bytecode 0x4a71afd9>)()
  calc-do(#f(compiled-function () #<bytecode 0x4a71afd9>) 126)
  calc-evaluate(1)
  funcall-interactively(calc-evaluate 1)
  call-interactively(calc-evaluate nil nil)
  command-execute(calc-evaluate)

bug#35374: Calc; Div by 0 in solving system

[Mattias Engdegård]

21 apr. 2019 kl. 17.37 skrev Christopher Howard <christopher.howard@qlfiles.net>:

> I enabled Debug on Error but could not find the backtrace

Reproduced in 26.1. Backtrace below.

I quickly got lost in calcalg2.el, but it looks like the equation

  2(z - 1.0) - (5 + 3(z - 1.0) - z) / 2 + 3z + 3 = 0,

isn't solved properly by math-try-solve-for: math-decompose-poly returns the correct decomposition of the LHS, (4) * z, but then the code decides to find a root of the polynomial (4) which of course doesn't exist and nothing good comes out of it. I'm not sure why the floating-point numbers (float 1 0) are there in the first place.

Maybe someone more knowledgeable about Calc can help further.

* math-reject-arg((float 1 0) "*Division by zero")
 math-div-by-zero((float 1 0) 0)
 math-div((float 1 0) 0)
 math-float((frac 1 0))
 math-mul((frac 1 0) (float 138629436111989 -14))
 math-mul-objects-fancy((frac 1 0) (cplx (float 138629436111989 -14) (float 314159265358979 -14)))
 math-mul((frac 1 0) (cplx (float 138629436111989 -14) (float 314159265358979 -14)))
 math-pow-fancy(-4 (frac 1 0))
 math-pow(-4 (frac 1 0))
 math-poly-laguerre-root((4) 0 t)
 math-poly-any-root((4) 0 t)
 math-try-solve-for((+ (+ (- (* 2 (- (var z var-z) (float 1 0))) (/ (- (+ 5 (* 3 (- (var z var-z) (float 1 0)))) (var z var-z)) 2)) (* 3 (var z var-z))) 3) 0 nil nil)
 math-try-solve-for((calcFunc-eq (+ (- (* 2 (- (var z var-z) (float 1 0))) (/ (- (+ 5 (* 3 (- (var z var-z) (float 1 0)))) (var z var-z)) 2)) (* 3 (var z var-z))) -3) 0 nil)
 math-solve-for((calcFunc-eq (+ (- (* 2 (- (var z var-z) (float 1 0))) (/ (- (+ 5 (* 3 (- (var z var-z) (float 1 0)))) (var z var-z)) 2)) (* 3 (var z var-z))) -3) 0 (var z var-z) nil)
 math-solve-system-rec((((calcFunc-eq (+ (- (* 2 (- (var z var-z) (float 1 0))) (/ (- (+ 5 (* 3 (- (var z var-z) (float 1 0)))) (var z var-z)) 2)) (* 3 (var z var-z))) -3))) ((var z var-z)) (((var y var-y) (- (var z var-z) (float 1 0))) ((var x var-x) (/ (- (+ 5 (* 3 (- (var z var-z) (float 1 0)))) (var z var-z)) 2))))
 math-solve-system-rec((((calcFunc-eq (- (+ (/ (- (+ 5 (* 3 (var y var-y))) (var z var-z)) 2) (var y var-y)) (* 2 (var z var-z))) 0)) ((calcFunc-eq (+ (- (* 2 (var y var-y)) (/ (- (+ 5 (* 3 (var y var-y))) (var z var-z)) 2)) (* 3 (var z var-z))) -3))) ((var y var-y) (var z var-z)) (((var x var-x) (/ (- (+ 5 (* 3 (var y var-y))) (var z var-z)) 2))))
 math-solve-system-rec((((calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5)) ((calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0)) ((calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3))) ((var x var-x) (var y var-y) (var z var-z)) nil)
 math-solve-system((vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z)) nil)
 calcFunc-solve((vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z)))
 apply(calcFunc-solve ((vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
 math-normalize((calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
 math-simplify((calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
 calc-normalize-fancy((calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
 calc-normalize((calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
 math-evaluate-expr((calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z))))
 mapcar(math-evaluate-expr ((calcFunc-solve (vec (calcFunc-eq (+ (- (* 2 (var x var-x)) (* 3 (var y var-y))) (var z var-z)) 5) (calcFunc-eq (- (+ (var x var-x) (var y var-y)) (* 2 (var z var-z))) 0) (calcFunc-eq (+ (- (* 2 (var y var-y)) (var x var-x)) (* 3 (var z var-z))) -3)) (vec (var x var-x) (var y var-y) (var z var-z)))))
 #f(compiled-function () #<bytecode 0x4a71afd9>)()
 calc-do(#f(compiled-function () #<bytecode 0x4a71afd9>) 126)
 calc-evaluate(1)
 funcall-interactively(calc-evaluate 1)
 call-interactively(calc-evaluate nil nil)
 command-execute(calc-evaluate)