Subversion Repositories wimsdev

!! this file is an annex for anstype litexp (or other)

!! some debugging information is stored in variable debuginfo, may be erased in a few months after 2024.05.01

!! see documentation at end of file

debuginfo=Analyse de $wims_read_parm

!if factorcontent notwordof $(replyoption$i)

  debuginfo=$debuginfo sans factorcontent

!else

  debuginfo=$debuginfo avec factorcontent

!endif

allowedchar=!text mark (,),*,^,-,+,0,1,2,3,4,5,6,7,8,9,a,b,c,d,f,g,h,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,A,B,C,D,F,G,H,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z in $wims_read_parm

!! due to rawmath, only x,y,z are accepted letters

!!allowedchar=!text mark (,),*,^,-,+,0,1,2,3,4,5,6,7,8,9,x,y,z,X,Y,Z in $wims_read_parm

badpositions=!positionof char 0 in $allowedchar

!if $badpositions!=$empty

  badposition=!item 1 of $badpositions

  badchar=!char $badposition of $wims_read_parm

  wrong=badform usebadchar $badchar

!endif

debuginfo=$debuginfo $wrong

pg=!char 1 of ()

pd=!char 2 of ()

!!********** wims_read_parm is rawmath-formated user's answer

nb=!charcnt $wims_read_parm

!distribute item 0,1,0 into par,flag,par2

!reset factor lfactors exp content lcontent flagpard

operand=!exec maxima op($wims_read_parm)

wrp=!replace - by +2* in $wims_read_parm

!!********** partly avoid maxima's evaluation before op (^^ not simplified)

wrp=!replace internal * by ^^ in $wrp

operand=!exec maxima op($wrp)

operand=!replace internal ^^ by * in $operand

debuginfo=$debuginfo operande=$operand

k=1

!!********** read string until end or error

!while ($k<=$nb and $wrong=$empty) or $factor!=$empty   

  c=!char $k of $wims_read_parm

  cc=!char $[$k+1] of $wims_read_parm

  debuginfo=$debuginfo\

  $c

!!********* condition to decide that the end of the factor is attained

  !if  $k>$nb or ($c=* and $par=0 and ($pg isin $wims_read_parm or $operand!="+"))

	  debuginfo=$debuginfo factor=$factor, exp=$exp	  

    !if $factor!=$empty

      !if $mpar2>0

        wrong=badform fparenthesis $factor

        !break

      !else

!!********* test to decide if factor contains a variable (NaN), then factorize it via pari (gets only polynomial factors, not the content,  ex : 2x^2-2  --> factor= x+1,1 ; x-1,1  )

        !if $[$factor*1]=NaN

  	  debuginfo=$debuginfo il contient une variable,

!!********* The old line about content is now useless because we test below that factor is irreducible (hence without content)

!!********* if factor is a power, remove the power (use maxima op, hence first remove - sign, replace temporarily by unused letter e)

          Nfactor=!replace - by +e in $factor

          foperand=!exec maxima op($Nfactor)

	  !if $foperand="^"

	    factor=!exec maxima part($Nfactor,1)

	    factor=!replace +e by - in $factor

	    factor=!replace e by - in $factor

	    exp=!exec maxima part($Nfactor,2)

	    exp=!replace +e by - in $exp

	    exp=!replace e by - in $exp

	  debuginfo=$debuginfo (factor=$factor, exp=$exp) 

	  !endif

          t1=!exec pari factor($factor)

	  debuginfo=$debuginfo pari donne la factorisation $t1

!!********* The old line "!replace internal -1,1; by $empty" is removed, because useless (since pari gives only non constant factors, hence never (-1)^1), and even inappropriate if factorization is x-1,1.

          tt1=!rowcnt $t1

!!********* Check that current factor is irreducible (equal up to sign to unique factor of its pari-factorization). Content check is useless.

          prime=!item 1 of $t1

	  exp=!item 2 of $t1

	  isirred=!exec maxima expand((($prime)-($factor))*(($prime)+$factor))

          debuginfo=$debuginfo  $factor prime=$prime isirred=$isirred 

          !if $tt1!=1 or $isirred!=0

            wrong=badform notcomplete $factor

	    debuginfo=$debuginfo  notcomplete 

          !else

!!********* If current factor not correctly expanded, this is reported in variable wrong by file expandpolynome.

            !read oef/analyse/expandpolynome $factor

	    debuginfo=$debuginfo  on teste via expandpolynome

          !endif

!!********* send error if current factor is already in list, add it otherwise

          !if $prime isitemof $lfactors

            wrong=badform multifactor $prime

          !else

            lfactors=!append item $prime to $lfactors

          !endif

        !else

	    debuginfo=$debuginfo  il est numérique

          !if factorcontent notwordof $(replyoption$i)

!!********* When no option factorcontent, check that the current numerical factor is the first one (only one is allowed), and not equal to 1

            !if $content!=$empty

              wrong=badform twofactorcst $content $factor

            !endif

	      !default exp=1

            !if $[($factor)^$exp]=1 and  $[$$wims_read_parm]!=1

  	      wrong=badform uselessfactor

	      !break

	    !endif

            content=$factor

          !else

!!********* When option factorcontent, we check that the current numerical factor has only one prime factor (apart sign)

            tmp=!exec pari factor($factor)

            tmp=!replace internal -1,1; by $empty in $tmp

            tt1=!rowcnt $tmp

            !if $tt1!=1

              wrong=badform factorcontent $factor

	    !else

	      !default exp=1

              debuginfo=$debuginfo factor^exp= $factor^$exp=$[($factor)^$exp]

	      !if $[($factor)^$exp]=1 and  $[$$wims_read_parm]!=1

	        wrong=badform uselessfactor

		!break

	      !endif

	      premier=!item 1 of $tmp

	      !if $premier=matrix(0,2)

	        premier=1

	      !endif

	      premierf=!replace \^.* by in $factor

	      !if ($premier!=$premierf) and (-$premier!=$premierf)

                debuginfo=$debuginfo premier=$premier, premierf=$premierf

                wrong=badform factorcontent $factor

              !endif

	      !if $premier isitemof $lcontent

                wrong=badform multifactor $premier

              !else

                lcontent=!append item $premier to $lcontent

              !endif

              debuginfo=$debuginfo tmp=$tmp lcontent=$lcontent

            !endif

          !endif

        !endif

        !reset factor exp flagpard

        mpar2=0

      !endif

    !endif

    flag=1

  !else

    debuginfo=$debuginfo factor=$factor   exp=$exp  par=$par  par2=$par2  mpar2=$mpar2 wrong=$wrong c=$c

!!********** condition on  pg because x-1 or 2x-1 alone is a correct factorization.

    !if $c isin +- and $par=0 and $factor!=$empty and  $pg isin $wims_read_parm

      debuginfo=$debuginfo notfactorised $k

      wrong=badform notfactorised $k

      factor=

    !else

      !if $c notin ()

        !if $c=^

          exp=0

          flagexp=1

          !if $flagpard=$empty

            factor=$factor$c

	  !endif

        !else

          !if $exp=$empty

            debuginfo=$debuginfo ajout de $c  

            factor=$factor$c

          !else

	    !if ($c isin 0123456789)

	      !if ($flagexp=1)

                exp=$exp$c

	      !endif

	    !else

	      flagexp=0

	    !endif

!!********** we continue the construction of current factor

            !if $flagpard=$empty or $operand="+"

              debuginfo=$debuginfo encore ajout de $c  

              factor=$factor$c

            !endif

          !endif

        !endif

      !else

        !if $c=$pg

          !if $flag=0 or $par>0

            !increase par2

            mpar2=$par2

          !endif

          !if (($par>0 or $par2>0) and $exp=$empty) or $operand="+"

            debuginfo=$debuginfo on ajoute $c  

            factor=$factor$c

          !endif

          !increase par

          flag=1

        !else

	  debuginfo=$debuginfo pardroite

	  flagpard=1

	  !if $mpar2>0

	    mpar2=$[$mpar2-1]

	    par2=$[$par2-1]

	  !endif

	    par=$[$par-1]

          !if (($par>0 or $par2>0) and $exp=$empty) or $operand="+"

            factor=$factor$c

          !endif

          debuginfo=$debuginfo envoi pour test de $factor

          !if $par2>0

            par2=$[$par2-1]

          !endif

          flag=0

        !endif

      !endif

    !endif

  !endif

  !increase k

  debuginfo=$debuginfo\

  endwhile $c $k/$nb, wrong=$wrong, factor=$factor

!endwhile

!exit

!if $wrong!=$empty

!!debug $debuginfo\

  sortie avec wrong=$wrong

!endif

Nothing is read by wims after this point, it is just here for information

To debug this file, put the !exit command 5 lines below.

Documentation

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

This file checks whether wims_read_parm is a factorized polynomial of Z[X] (or any variable except e,E,i,I),

each factor being simplified as described in file expandpolynome of this directory.

It assumes that wims_read_parm has been formated by the rawmath function (as is done in the file litexp),

so is presented with * between factors and without spaces.

errors checked (for factor):

- notcomplete : a factor is not completely factorised

- multifactor : a factor is repeated instead of using power

- twofactorcst : the constant factor is not unique (when no option factorcontent)

- factorcontent : content of the polynome is not factorized (when option factorcontent)

- notfactorised : expression is not a product

- usebadchar : forbidden characters used in polynomial (like /.eEiI) the letters e,E,i,I have a numerical value when wims calls pari

- uselessfactor : factor has value 1 (not always checked)

- fparenthesis  : factor contains a parenthesis

some variables :

par is number of not yet closed left parenthesis when scanning the expression

mpar2 is maximal number of parentheses attained in the factor (should be 0 if simplified)

lfactors is current list of non constant irreducible factors

content is empty until some constant factor is found (used when no option factorcontent)

lcontent is current list of constant prime factors (used when option factorcontent)

exp is the exponent (number following ^)

flagpard used to decide whether exp is part of factor itself.

allowedchar is the list of allowed characters in the expression.

            e,E,i,I should be forbidden because they have numerical value in pari factorization.

	    Letters other than x,y,z are considered as function names by rawmath when in front of a left parenthesis. Hence x(x+1) and (u-1)(u+1) are ok as polynomials, but not u(u+1).

	    Since some exercises (H2/algebra/OEFevalwimslitt.fr) already use letter b, all letters except e,i are allowed, but the documentation should mention this behavior :

	    it is not safe to use letters other than x,y,z in the good answer if it is not given in machine-understandable format.

	    We could change this behavior via a new option (strictvar, to limit variable names to x,y,z).

	    Users might be tempted t use / or .  because they are common (ex : 15.0/3*x^2) but fthey are forbidden because too difficult to treat in this file.

How does it work?

- We first check there are only allowed characters in the expression

- Then we read the string character by character, to find the factors. Because the input comes from rawmath, the factors are separated by a *.

  Hence the general idea is that a factor ends when it is followed by a *, except if we are inside a pair of parentheses : 2 is a factor in 2*(x+1) but not in 3*(2*x+1)

  But this is not always correct : 2 is not a factor in 2*x+1 or 2*(x+1)*(x+2)-1. In general it is not possible to be sure that a factor ends before we read the entire expression (and write it as a tree).

  This is why we use the maxima "op" operator (which does the tree job), to know if the entire expression is a sum or a product. If it is a sum, the only factor is the entire expression.

  We have to cheat to use op because maxima evaluate op's argument : (-1)*(x-1) is a sum.

  If it is a product, we apply the general idea above. 

- Once we have found a factor, we treat separately the cases of a nonconstant or constant factor : 

  - for nonconstant factor (NaN), check that it is irreducible (equal up to sign to unique factor of its pari-factorization), correctly expanded (using file expandpolynome) and new (not in lfactors).

  - for constant factor, separate in 2 cases depending on option factorcontent :

    - without option factorcontent check that it is new and not of value 1.

    - with option factorcontent check that it is primary, power of a new prime, and not of value 1.

- As soon as some error is found, it is stored in the variable wrong and we exit

To check this file, try the following exercise, with 6*(x-1)*(x+1) replaced by any other polynomial in machine understandable format.

You may try natural format (like 6(x-1)(x+1)) for user's answer

\text{P=6*(x-1)*(x+1)}

\statement{Factorize P=\P}

\answer{without option factorcontent }{\P}{type= litexp}{option=polfactor}

\answer{with option factorcontent}{\P}{type= litexp}{option=polfactor,factorcontent}

We comment here some examples for P, depending on option factorcontent (yes,no,any)

Correctly accepted :

P                    factorcontent         remarks

1                    any

-2                   any

-x                   any

-2x                  any

8x                   no

2^3x                 yes

-8x                  no

-2^3x                yes

x^3                  any

-x^3                 any

x^(3)                any

2(x-1)               any

(x-1)2               any

(x-1)^2              any

-(x-1)^2             any

x^2+1                any                   bug in original : blocked

x^2+x+1              any                   bug in original : blocked

2x(1-x)(x+1)         any

y(y+1)               any

a-1                  any                   bug in original : blocked

-1(1-a)              any

-(1-a)               any

-(x-1)               any

Correctly blocked :

P                             factorcontent    reason                       remarks

4-2                           yes              factorcontent 4-2

8x                            yes              factorcontent 8              bug in original : accepted

2*2*2*x                       no               twofactorcst 2 2

2*2*2*x                       yes              multifactor 2                bug in original : accepted

-2*2                          no               twofactorcst -2 2

-2*2                          yes              multifactor 2                bug in original : accepted

2^3 2^2x                      no               twofactorcst 2^3 2^2

2^3 2^2x                      yes              multifactor 2                bug in original : accepted

(-1)(x-1)(x+1)(-1)            no               twofactorcst -1 -1

(-1)(x-1)(x+1)(-1)            yes              multifactor -1               bug in original : accepted

(-1)(x-1)(x+1)((-1))          no               twofactorcst -1 (-1)

(-1)(x-1)(x+1)((-1))          yes              multifactor -1

(x^2-1)                       any              notcomplete (x^2-1)          bug in original : accepted

x^2-1, -2x(x^2-1)             any              notcomplete x^2-1            bug in original : bad reasons

2.0*x                         any              usebadchar .                 different reason  in original (accepted if no)

2?0*x                         any              usebadchar ?                 exercise error in original

2/1*x                         any              usebadchar /                 usedivide in original

2*x-1*1                       any              notreduced termenumsimp -1*1

2x(1-x)2(x+1)                 no               twofactorcst 2 2

2x(1-x)2(x+1)                 yes              multifactor 2                bug in original : accepted 

2x(1-x)1(x+1)                 any              uselessfactor                

(-1)^2(x-1)(x+1)              any              uselessfactor                accepted in original

2*x*3^0                       any              uselessfactor

x^2+2x+1                      any              notcomplete x^2+2*x+1        bad reason in original

x(x^2+2x+1)                   any              notcomplete x^2+2*x+1        bad reason in original

2(x+1)-1                      any              notfactorised 8

(x+1)x(x+1)                   any              multifactor x+1

(x+1)(-1-x)                   any              multifactor x+1

-2(1-x)(x^2+x+1-x^2)x         any              notreduced termesamepower x^2,-x^2    bad reason in original

(x+1)^3*(x+1)^(-1)            any              multifactor x+1              different reason in original

-14y(-11y+15)+2y(-11y+15)     no               notfactorised 17

6x(x-1)+1                     no               notfactorised 10

6x(x-1)+1                     yes              factorcontent 6

2*(1+(x+1))                   any              notreduced parenthesis

Correctly blocked, but for bad reason (bug) :

P                             factorcontent    reason                            remarks

(x-1)*1                       any              notreduced parenthesis

x^(2x+1)                      any              notcomplete x^2*x+1               P is not a polynomial, factor is wrong

x^2*x+1                       any              notcomplete x^2*x+1               bad reason in original

3^(2+1)                       yes              factorcontent 3^2+1               factor is wrong. Accepted in original

-14y(-11y+15)+2y(-11y+15)     yes              factorcontent -14                 

Wrongly accepted (bug):

P                    factorcontent

Wrongly blocked (bug):

P                    factorcontent    reason                     remarks

Accepted, but not sure it is what we want

P                    factorcontent        remarks

2^3x                 no                   the constant factor is not computed, but still accepted.

(-1)^3x              any                  correct but not simplest form

3^(2+1)              no                   constant not completely computed

4-2                  no                   constant not completely computed. Blocked in original

2^(1+0)              any

3^(7+7)x             no                   clearly not simplest form

(2)                  any                  compare with (x+1) which is blocked

(x)                  any                  compare with (x+1) which is blocked

b^(3-3)*(a-1)        any                  the letter b is not in the good answer.

(b-1)^(3-3)*(a-1)    any                  blocked in original

Blocked, but not sure it is what we want

P                    factorcontent        reason                     remarks

(x+1)                any                  notreduced parenthesis     accepted in original (better?)

Yet to be tested

P                    factorcontent        reason                     remarks

known bugs :