factor(5x^4 + 20x^3 - 62x^2 - 8x +24)

TI 200 returns
(x-2)(x+6)(5x^2-2)

HP Prime returns
(x-2)(x+sqroot(10)/5)(x+6)(5x-sqroot(10))

Anyway to have the Prime avoid the sqroots?

Uncheck 'Use ¡Ô ' in the CAS settings before doing the above factorisation.

Edited: 29 Oct 2013, 12:11 p.m.

Worked okay for me if CAS Settings set to:

"Use sqrt to factor polynomials" set to UNCHECKED and "Simplify" set to NONE or MINIMUM.

Best,
Carl

Here is a perfect example for the recent "collect vs factor" discussion! :-)

Collect will return the same result as the TI, while factor will completely factor it as far as possible due to having more capable factoring capabilities.

TW

Edited: 29 Oct 2013, 12:19 p.m.

Thanks Tim! It looks like you can also control the "extent" of terms COLLECTION by adjusting the CAS Simplify settings? Cool.

Quote:

---

Here is a perfect example for the recent "collect vs factor" discussion! :-)

Collect will return the same result as the TI, while factor will completely factor it as far as possible due to having more capable factoring capabilities.

TW

---

collect == factor =(

Collect (HP-Prime) this factoring in most cases and is not doing what it says catalog help.

[ HP-PRIME CAS MODE & APPROX MODE ]

collect( (-3*a*x^2 +7*a*x^1 -2*a-3*b*x^2 + 7*b*x^1 -2*b+3*x^3 -7*x^2 + 2*x^1)/3 ) ; [ENTER] => -1.*(x-2.)*(x-0.333333333333)*(a-x+b)

factor( (-3*a*x^2 +7*a*x^1 -2*a-3*b*x^2 + 7*b*x^1 -2*b+3*x^3 -7*x^2 + 2*x^1)/3 ) ; [ENTER] => -1.*(x-2.)*(x-0.333333333333)*(a-x+b)

[ HP-PRIME CAS MODE & EXACT MODE ]

collect( (-3*a*x^2 +7*a*x^1 -2*a-3*b*x^2 + 7*b*x^1 -2*b+3*x^3 -7*x^2 + 2*x^1)/3 ) ; [ENTER] => (x-2)*(3*x-1)*(x-a-b)/3

factor( (-3*a*x^2 +7*a*x^1 -2*a-3*b*x^2 + 7*b*x^1 -2*b+3*x^3 -7*x^2 + 2*x^1)/3 ) ; [ENTER] => (x-2)*(3*x-1)*(x-a-b)/3

My collect

collectPolTerms( (-3*a*x^2 +7*a*x^1 -2*a-3*b*x^2 + 7*b*x^1 -2*b+3*x^3 -7*x^2 + 2*x^1)/3, x ) ; =>

x^3 + ((-3*a-3*b-7)/3)*x² +((7*a+7*b+2)/3)*x + (-2*a-2*b)/3*x^0 // :) OK

more info

http://www.adictoshp.org/topic/473-casplus-library-for-hp-prime

source code cas+ with real collect poly

main( ):=

BEGIN

	CONJUGATE() := BEGIN true; END;

	SYMBOLIC() := BEGIN true; END;

	RETURN( OK );

END;

collectPolTerms( Poly, Var ):=

BEGIN

	LOCAL FlagBadArg;

	FlagBadArg:= "false";

	IF NOT( POS( { "AlgExpression", "Equation", "Identifier", "RealNumber", "IntegerNumber", 

	"AlgComplexNumber", "RationalNumber", "RatComplexNumber" }, getType( Poly ) ) )

	THEN

		FlagBadArg := "true";

		IF NOT( MSGBOX( "collectPolTerms:Invalid Data Type for 1 arg", true ) )

		THEN kill;

		END;

	END;

	IF NOT( getType( Var ) == "Identifier" )

	THEN

		 FlagBadArg := "true";

		 IF NOT( MSGBOX( "collectPolTerms:Invalid Data Type for 2 arg", true ) )

		 THEN kill;

		 ELSE kill;

		 END;

	END;

	IF FlagBadArg == "false"

	THEN

		IF isEquation( Poly ) == "true"

		THEN

			Poly := toEq( eqToExpr );

		END;

		RETURN( sum( coeff( Poly, Var ) .* seq( Var^k, k, degree( Poly, Var ), 0, 1 ) ));

	ELSE

		RETURN( "Invalid Data Type" );

	END;

END;

getType( Data0 ):=

BEGIN

	LOCAL TypeN, TypeID, RealType, ObjStr;

	TypeID := type( Data0 );

	IFERR

		TYPE( Data0 )

	THEN

		RealType := "ERROR";

		ObjStr := "ERROR";

	ELSE

		TypeN := TYPE( Data0 );

		ObjStr := STRING( Data0 );

	END;

	CASE

		IF TypeID == DOM_FLOAT

		THEN

			RealType := "RealNumber";

		END;

		IF TypeID == DOM_INT

		THEN

			RealType := "IntegerNumber";

		END;

		IF TypeID == DOM_COMPLEX

		THEN

			IF inString( ObjStr,"(" ) >= 1

			THEN

				RealType := "CooComplexNumber";

			ELSE

				RealType := "AlgComplexNumber";

			END;

		END;

		IF TypeID == DOM_RAT

		THEN

			IF inString( ObjStr, string( i ) ) >= 1

			THEN

				RealType := "RatComplexNumber";

			ELSE

				RealType := "RationalNumber";

			END;

		END;

		IF TypeID == DOM_SYMBOLIC

		THEN

			IF inString( string( Data0 ), "=" ) >= 1

			THEN

				RealType := "Equation";

			ELSE

				RealType := "AlgExpression";

			END;

		END;

		IF TypeID == DOM_IDENT

		THEN

			RealType := "Identifier";

		END;

		IF TypeID == DOM_STRING

		THEN

			RealType := "String";

		END;

		IF TypeID == DOM_FUNC

		THEN

			RealType := "Function";

		END;

		IF TypeID == DOM_LIST

		THEN

			CASE

				IF inString( ObjStr, "poly1[" ) >= 1

				THEN

					RealType := "PolynomialCoeff";

				END;

				IF inString( ObjStr, "set[" )>= 1

				THEN

					RealType := "Set";

				END;

				IF inString( ObjStr, "[[" ) >= 1

				THEN

					RealType := "Matrix";

				END;

				IF inString( ObjStr, "[" ) >= 1

				THEN

					RealType := "Vector";

				END;

				IF inString( ObjStr, "{" ) >= 1 OR inString( ObjStr, "{[" ) >= 1

				THEN

					RealType := "List";

				END;

				DEFAULT RealType := "Other Type LIST";

			END;

		END;

		IF TypeN == 8

		THEN

			RealType := "Unit";

		END;

		IF TypeID == 21

		THEN

			RealType := "HMS";

		END;

		IF TypeN == 1

		THEN

			CASE

				IF inString( ObjStr, "d" ) >= 1

				THEN

					RealType := "DecNumber";

				END;

				IF inString( ObjStr, "b" ) >= 1

				THEN

					RealType := "BinNumber";

				END;

				IF inString( ObjStr, "h" ) >= 1

				THEN

					RealType := "HexNumber";

				END;

				IF inString( ObjStr, "o" ) >= 1

				THEN

					RealType := "OctNumber";

				END;

				DEFAULT RealType := "Other Base";

			END;

		END;

		DEFAULT RealType := "Other";

	END;

	RETURN( RealType );

END;

partString( Str0, StrP ):=

BEGIN

	LOCAL FlagBadArg;

	FlagBadArg:= "false";

	IF NOT( ( getType( Str0 ) == "String" ) AND ( NOT( Str0 == "" ) ) )

	THEN

		FlagBadArg := "true";

		IF NOT( MSGBOX( "partString: Invalid Data Type for 1 Arg", true ) )

		THEN kill;

		END;

	END;

	IF NOT( ( getType( StrP ) == "String" ) AND ( NOT( StrP == "" ) ) )

	THEN

		FlagBadArg := "true";

		IF NOT( MSGBOX( "partString: Invalid Data Type for 2 Arg", true ) )

		THEN kill;

		ELSE kill;

		END;

	END;

	IF FlagBadArg == "false"

	THEN

		RETURN( convertToRealBoolean( inString( Str0, StrP ) ) );

	ELSE

		RETURN( "Invalid Data Type" );

	END;

END;

convertToRealBoolean( Object0 ):=

BEGIN

	IF isBooleanDataType( Object0 ) == "true"

	THEN

		IF getType( Object0 ) == "String"

		THEN

			Object0 := expr( Object0 );

		END;

		IF Object0 <= 0

		THEN

			RETURN( "false" );

		ELSE

			RETURN( "true" );

		END;

	ELSE

		IF NOT( MSGBOX( "convertToRealBoolean: Invalid Data Type", true ) )

		THEN kill;

		ELSE kill;

		END;

	END;

END;

isBooleanDataType( Object ):=

BEGIN

	LOCAL FlagBadArg, ObjectType;

	FlagBadArg:= "false";

	ObjectType := getType( Object );

	IF NOT( POS( { "RealNumber", "IntegerNumber", "RationalNumber", "String" }, ObjectType ) )

	THEN

		FlagBadArg := "true";

	END;

	IF FlagBadArg == "true"

	THEN

		RETURN( "false" );

	ELSE

		IF ObjectType == "String"

		THEN

			ObjectType:= expr( Object );

			IF isNumber( ObjectType ) == "true"

			THEN RETURN( "true" );

			ELSE RETURN( "false" );

			END;

		ELSE

			RETURN( "true" );

		END;

	END;

END;

isNumber( Object ):=

BEGIN

	LOCAL ObjectType;

	ObjectType:= getType( Object );

	IF POS( { "RealNumber", "IntegerNumber", "RationalNumber" }, ObjectType )

	THEN

		RETURN( "true" );

	ELSE

		RETURN( "false" );

	END;

END;

isComplexNumber( Object ):=

BEGIN

	LOCAL ObjectType;

	ObjectType:= getType( Object );

	IF POS( { "CooComplexNumber", "AlgComplexNumber", "RatComplexNumber" }, ObjectType )

	THEN

		RETURN( "true" );

	ELSE

		RETURN( "false" );

	END;

END;

isEquation( Object ):=

BEGIN

	LOCAL FitObject;

	IFERR

		EVAL( Object );

	THEN

		FitObject := Object;

	ELSE

		FitObject :=  EVAL( Object );

	END;

	IF getType( FitObject ) == "Equation"

	THEN

		RETURN( "true" );

	ELSE

		RETURN( "false" );

	END;

END;

eqToExpr( Eq ):=

BEGIN

	IF isEquation( Eq ) == "true"

	THEN

		RETURN( expr( replace( string( Eq ), "=" , "-(" ) + ")" ) );

	ELSE

		RETURN( Eq );

	END;

END;

transpose2( Array, Test0 ):=

BEGIN

	LOCAL FlagBadArg;

	FlagBadArg:= "false";

	IF NOT( POS( { "Vector", "Matrix" }, getType( Array ) ) )

	THEN

		FlagBadArg := "true";

		IF NOT( MSGBOX( "transpose2: Invalid Data Type for 1 arg", true ) )

		THEN kill;

		END;

	END;

	IF NOT( isBooleanDataType( Test0 ) == "true" )

	THEN

		FlagBadArg := "true";

		IF NOT( MSGBOX( "transpose2: Invalid Data Type for 2 arg", true ) )

		THEN kill;

		ELSE kill;

		END;

	ELSE

		Test0 := convertToRealBoolean( Test0 );

	END;

	IF FlagBadArg == "false"

	THEN

		IF Test0 == "true"

		THEN

			RETURN( TRN( Array ) );

		ELSE

			RETURN( transpose( Array ) );

		END;

	ELSE

		RETURN( "Invalid Data Type" );

	END;

END;

toPoly1var( Object, Var, Test ):=

BEGIN

	LOCAL FlagBadArg, FitPoly, ObjectType;

	FlagBadArg:= "false";

	ObjectType := getType( Object );

	IF NOT( POS( { "AlgExpression", "Equation", "Identifier", "RealNumber", "IntegerNumber",

		"AlgComplexNumber", "RatComplexNumber", "RationalNumber", "PolynomialCoeff", "Vector" }, ObjectType ) )

	THEN

		FlagBadArg := "true";

		IF NOT( MSGBOX( "toPoly1var: Invalid Data Type for 1 arg", true ) )

		THEN kill;

		END;

	END;

	IF NOT( getType( Var ) == "Identifier" )

	THEN

		FlagBadArg := "true";

		IF NOT( MSGBOX( "toPoly1var: Invalid Data Type for 2 arg", true ) )

		THEN kill;

		END;

	END;

	IF NOT( isBooleanDataType( Test ) == "true" )

	THEN

		FlagBadArg := "true";

		IF NOT( MSGBOX( "toPoly1var: Invalid Data Type for 3 arg", true ) )

		THEN kill;

		ELSE kill;

		END;

	ELSE

		Test := convertToRealBoolean( Test );

	END;

	IF FlagBadArg == "false"

	THEN

		CASE

			IF ObjectType == "PolynomialCoeff"

			THEN

				IF Test == "true"

				THEN

					RETURN( poly2symb( ObjectType, Var ) );

				ELSE

					RETURN( ObjectType );

				END;

			END;

			IF ObjectType == "Vector"

			THEN

				FitPoly := expr( "poly1" + Object );

				IF Test == "true"

				THEN

					RETURN( poly2symb( FitPoly, Var ) );

				ELSE

					RETURN( FitPoly );

				END;

			END;

			IF isEquation( Object ) == "true"

			THEN

				FitPoly := eqToExpr( Object );

				IF Test == "false"

				THEN

					RETURN( symb2poly( FitPoly, Var ) );

				ELSE

					RETURN( FitPoly );

				END;

			END;

			DEFAULT

				IF Test == "false"

				THEN

					RETURN( symb2poly( Object, Var ) );

				ELSE

					RETURN( Object );

				END;

		END;

	ELSE

		RETURN( "Invalid Data Type" );

	END;

END;

polyCoeffToArray( Poly ):=

BEGIN

	LOCAL FlagBadArg;

	FlagBadArg:= "false";

	IF NOT( POS( { PolynomialCoeff }, getType( Poly ) ) )

	THEN

		FlagBadArg := "true";

		IF NOT( MSGBOX( "polyCoeffToArray: Invalid Data Type for 1 arg", true ) )

		THEN kill;

		END;

	END;

	IF FlagBadArg == "false"

	THEN

		RETURN := expr( replace( string( Poly ), "poly1" , "" )  );

	ELSE

		RETURN( "Invalid Data Type" );

	END;

END;

randPoly2( Pdim, Il, Sl, Var, Test ):=

BEGIN

	LOCAL Rp;

	Rp := randPoly( Pdim, expr( Il + ".." + Sl ) );

	RETURN( toPoly1var( Rp, Var, Test ));

END;

polyToCoeff( Poly, Var ):=

BEGIN

	LOCAL PolyFnt, Out, Cnt0, Temp0;

	purge( Pol );

	IF isEquation( Poly ) == "true"

	THEN

		Poly := eqToExpr( Poly );

	END;

	expr( Pol(Var)+":="+string( Poly ) );

	Out := MAKELIST( 0, Cnt1, degree( Poly ), 0, 1 );

	Cnt0:=0;

	WHILE Pol(Var) <> 0 DO

		Temp0 := Pol(Var) / (Cnt0!) ;

		Out[ Cnt0 ] := ( Temp0 | Var=0 );

		Cnt0 := Cnt0 + 1;

		Pol(Var) := diff( Pol(Var), Var);

	END;

	Out := expr( "poly1[" + string( REVERSE(Out) ) + "]");

	RETURN( Out );

END;

 

Edited: 29 Oct 2013, 4:36 p.m. after one or more responses were posted

Thanks Tim! It looks like you can control the "extent" of terms COLLECTION(or FACTORING) by adjusting the CAS Simplify settings? Again, Cool

Re: HP-Prime vs TI-CAS (calculators): Factoring

TI-CAS: TI92(+)/TI89(TITANIUM)/TIvoyage200/TInspire[CX]CAS/...

HP-CAS: HP-Prime/HP50G

[TI-CAS: EXACT MODE]

factor(5*x^4+20*x^3-62*x^2-8*x+24,x) [ENTER] RETURN

(x-2)*(x+6)*(5*x^2-2)

[TI-CAS: APPROXIMATE MODE]

factor(5*x^4+20*x^3-62*x^2-8*x+24,x) [ENTER] RETURN

5.*(x-2.)*(x-0.632455532034)*(x+0.632455532034)*(x+6.)

[TI-CAS: AUTOMATIC MODE]

factor(5*x^4+20*x^3-62*x^2-8*x+24,x) [ENTER] RETURN

(x-2)*(x+6)*(5*x^2-2)

////////////

[HP-CAS: EXACT MODE & NONE SIMPLIFY]

factor(5*x^4+20*x^3-62*x^2-8*x+24,x) [ENTER] RETURN

(x-2)*(x+6)*(5*x^2-2)

[HP-CAS: APPROXIMATE MODE & NONE SIMPLIFY]

factor(5*x^4+20*x^3-62*x^2-8*x+24,x); [ENTER] RETURN

5.*(x-2.)*(x-0.632455532034)*(x+0.632455532034)*(x+6.)

[HP-CAS: EXACT MODE & MAX SIMPLIFY]

factor(5*x^4+20*x^3-62*x^2-8*x+24,x); [ENTER] RETURN

5*x^4+20*x^3-62*x²-8*x+24 BUG

IF MAX_SIMPLIFY == ON THEN SKIP FLAG...

...

factor(y^3+(a+b+c)*y²+(a*b+b*c+c*a)*y+a*b*c,y); => (y+c)*(y+b )*(y+a)

factor(y²+(a+b )*y+a*b,y);(y+b )*(y+a)

cfactor(x^3-y^3,y) ? //

Edited: 29 Oct 2013, 3:47 p.m.