| 1,108 → 1,402 |
|---|
| !! this file is an annexe for anstype litexp (or other) |
| !! it look if wims_read_parm is a factorised polynome of Z[X] |
| !! each factor as to be simplified as describe in file expandpolynome of this directory |
| !! |
| !! error 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 calculated (in case of non use of optionword factorcontent) |
| !! - factorcontent : content of the polynome is not factorised (in case of use of optionword factorcontent) |
| !! - notfactorised : expression is not a product |
| !! - usedivide : use of symbol / |
| !! 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 $wims_read_parm |
| !distribute item 0,1,0 into par,flag,par2 |
| !reset factor lfactors notfactor exp content |
| !reset factor lfactors exp content lcontent flagpard |
| operand=!exec maxima op($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=$operand |
| k=1 |
| !while ($k<=$nb and $wrong=$empty) or $factor!=$empty |
| !!********** read string until end or error |
| !while ($k<=$nb and $wrong=$empty) or $factor!=$empty |
| c=!char $k of $wims_read_parm |
| !if ($c=* and $par=0) or $k>$nb |
| 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 |
| tmp=!exec pari factor($factor)\ |
| content($factor) |
| !distribute line $tmp into t1,t2 |
| t1=!replace internal -1,1; by $empty in $t1 |
| debuginfo=$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 |
| !if $tt1!=1 or $t2!=1 |
| !!********* 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 |
| !endif |
| !if $wrong=$empty |
| 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 |
| tmp1=!item 1 of $t1 |
| !if $tmp1 isitemof $lfactors |
| wrong=badform multifactor $tmp1 |
| !!********* send error if current factor is already in list, add it otherwise |
| !if $prime isitemof $lfactors |
| wrong=badform multifactor $prime |
| !else |
| lfactors=!append item $tmp1 to $lfactors |
| 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 |
| !reset factor exp flagpard |
| mpar2=0 |
| !endif |
| !endif |
| flag=1 |
| !else |
| !if $c isin +- and $par=0 and $factor!=$empty |
| 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=/ |
| wrong=badform usedivide |
| !else |
| !if $c notin () |
| !if $c=^ |
| exp=0 |
| !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 $exp=$empty |
| !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$c |
| !else |
| exp=$exp$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 |
| !if $c=$pg |
| !if $flag=0 or $par>0 |
| !increase par2 |
| mpar2=$par2 |
| !endif |
| !if ($par>0 or $par2>0) and $exp=$empty |
| factor=$factor$c |
| !endif |
| !increase par |
| flag=1 |
| !else |
| par=$[$par-1] |
| !if ($par>0 or $par2>0) and $exp=$empty |
| factor=$factor$c |
| !endif |
| !if $par2>0 |
| par2=$[$par2-1] |
| !endif |
| flag=0 |
| debuginfo=$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 : |
| |