[CAS:HP-PPL] Total control of flags to successfully run a program

[compsystems]

Hello, the following code fails if the "increasing" flag is set

The evolution of the HP-PPL is going in a right way, but this should improve.
The handling of expression with PART cmd is affected by the cas flags, for this reason I should be able to source code to set them

Expr -> 9 * x ^ 2 + 8 * x (increasing off)
Part (expr, 1) -> 9 * x ^ 2

Expr -> 8 * x + 9 * x ^ 2 (increasing on)
Part (expr, 1) -> 8 * x

I can not tell the user to prefix manually n flags before running the program, the control of flag must be automatic and by commands,
with the currently HP-PPL, I can not determine the status of some flags and the programs return incorrect answers
My recommendation is to complete the support of the flag shown in CAS settings ...

quadraticFormulaStepByStep source code
https://en.wikipedia.org/wiki/Quadratic_formula

PHP Code:

export exprout; // only test
#cas
    quadraticFormulaStepByStep():=
    BEGIN
    // version 0.9
    local expr0, expr1, expr2, expr3, coef; 
    local leftExpr, leftExpr1, leftExpr2, rightExpr, rightExpr1, rightExpr2;
    local part1, part2, part3;
    local degree2, degree1;
    part1:=1; part2:=2; part3:=3;
    degree2:=2; degree1:=1;
    purge(a,b,c,x);

    print;
    print( "DETERMINACIÓN DE LA FÓRMULA CUADRÁTICA" ); //Ecuación de segundo grado
    print( "Sea la función cuadrática en una variable:" );
    expr0:= a*x^2+b*x+c;
    print( "f(x) = " + expr0 );
    print( "" ); 
    print( "Soluciones:" );
    print( "x12 =-b/(2 a) ±√[b² -4 a c]/(2 a)" );
    print( "" ); 
    print( "Para hallar la fórmula cuadrática, aplicamos el método de completar cuadrados. Veamos:" );

    print( "" ); 
    print( "Step0: hacemos f(x)=0" );
    expr1:= expr0 = 0;
    print( string(expr1) );

    print( "" ); 
    print( "Step1: llevamos el termino independiente al lado derecho (restamos c) a ambos lados:" );
    leftExpr := part(expr1,part1) - c; // parte1 - c
    rightExpr := part(expr1,part2) - c; // parte2 - c
    expr1:= leftExpr = rightExpr;
    print( string(expr1) );
    print( "" );
    print( "Step1.1: simplificando a ambos lados de la ecuación:" );
    expr1:= simplify( expr1 );
    print( string(expr1) ); 

    print( "" ); 
    print( "Step2: llevando el coeficiente del termino cuadrático a 1; para esto se divide toda la ecuación por 'a'." );
    expr1:= expr1/a;
    print( string(expr1) );

    print( "" ); 
    print( "Step2.1: distribuyendo el denominador en el lado izquierdo de la ecuación:" );
    expr1:= expand( expr1 );
    print( string(expr1) ); 

    print( "" );
    print( "Step2.2: reorganizando coeficientes luego variable:" );
    //print( "Step2.3: simplificando el primer término del lado izquierdo de la ecuación:" );
    leftExpr:= part(expr1,part1); // a/a -> 1 

    leftExpr1:= coeff( part(leftExpr,part1), degree2)*x^2; //print( leftExpr1 ); wait();
    leftExpr2:= coeff( part(leftExpr,part2), degree1)*x; //print( leftExpr2 ); wait();
    rightExpr:= part(expr1,part2); 
    expr1:= leftExpr1 + leftExpr2 = rightExpr; 
    print( string(expr1) );

    print( "" ); 
    print( "Step3: Se extrae el coeficiente del termino lineal para completar cuadrados:" );
    coef:= coeff(leftExpr2,1);
    print( "coeficiente: " + coef ); 
    coef:= simplify(coef/2); // b/a/2 -> b/(2*a)

    print( "Se completa cuadrados en la ecuación:" );
    leftExpr := leftExpr1 + leftExpr2 + coef^2;
    rightExpr1:= coef^2;
    rightExpr2:= rightExpr; 
    rightExpr:= rightExpr1 + rightExpr2;
    expr1:= leftExpr = rightExpr;
    print( string(expr1) );
    print( "" ); 
    print( "Step4: llevando el lado izquierdo como un trinomio cuadrado perfecto" );
    print( "y distribuyendo el cuadrado el lado derecho:" );
    //factor
    rightExpr:= simplify(rightExpr1) + rightExpr2;

    expr2:= (x+coef); 
    expr1:= expr2^2 = rightExpr;
    print( string(expr1) );

    print( "" ); 
    print( "simplificando el lado derecho:" );
    leftExpr:= part(expr1,part1);
    rightExpr:= reorder(simplify(rightExpr),[b]); 
    expr1:= leftExpr = rightExpr;
    print( string(expr1) );

    print( "" );
    print( "Step5: extrayendo raíz cuadrada a la ecuación:" );
    //expr1:= √(leftExpr) = √(rightExpr);
    print( "√(" + leftExpr + ") =");
    print( "√(" + rightExpr + ")" );

    print( "" ); 
    print( "Step5.1: simplificando el lado izquierdo y distribuyendo √ lado derecho:" );
    expr2:= part(rightExpr,part1); //print( "numerator " + expr2 );

    expr3:= part (part( rightExpr,part2), 1); //print( "denominator " + expr3 );

    print( string(x+coef) + " = √[" + expr2 + "]/" + "√[" + expr3 + "]" );

    print( "" ); 
    print( "Step5.2: simplificando lado derecho:" );
    assume(a>0);
    expr3:=simplify(√(expr3));
    print( string(x+coef) + " = √[" + expr2 + "]/" + expr3 );

    print( "" ); 
    print( "Step5.3: Despejando x:" );
    print( "llevamos el termino independiente al lado derecho (restamos b/(2a)) a ambos lados:" );
    print( string(x+coef) + "-" + coef + " =" );
    print( string(-coef) + " + √[" + expr2 + "]/" + expr3 );

    print( "" ); 
    print( "Step6: Simplificando" );
    print( string(x) + " = " + -coef + " ± √[" + expr2 + "]/" + expr3 );


    print( "" ); 
    print( "Step6.1: Agrupando" );
        //

        purge(a);
    //exprout := expr1;
    return "done";
    //return exprout;
    END;
#end 


Think if the output of the program previous, would be observed in pretty-print



Other problems with the previous code


History view

(b^2-4*a*c)/(4*a^2); [enter] -> (b^2-4*a*c)/(4*a^2) // ok // part 1 -> b^2-4*a*c , part 2 -> 4*a^2

part(Ans,1); [enter] -> b^2-4*a*c // ok

-----------------------------------
(b^2-4*a*c)/(4*a^2); [enter] -> (b^2-4*a*c)/(4*a^2) // ok

part(Ans,2); [enter] -> 1/(4*a^2) // Why? I expected 4*a^2, Does not agree with the show history view, with the calculated:

part(Ans,1); [enter] -> 4*a^2 Why? The above expression says 1/(4*a^2), // part 1 -> 1 part 2 -> 4*a^2

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

(b^2-4*a*c)/(4*a^2); [enter] -> (b^2-4*a*c)/(4*a^2) // ok

part(Ans,2); [enter] -> 1/(4*a^2) // part 1 -> 1 , part 2 -> 4*a^2

part(Ans,2); [enter] -> "Error: Bad Argument Value"