Revision history [back]

simplification errors in simple expressions

I'm currently testing the possibilities of SAGE as a teaching aid in a high school math course (in Belgium). I stumbled upon this:

• When evaluating x/sqrt(x^2), SAGE answers $\frac{x}{|x|}$, as it should. Appending a .simpify()-instruction to the input does not change anything.
• However, ((1-x^2)/sqrt(1-2*x^2+x^4)).simplify_full() evaluates to $-1$, in stead of $\frac{1-x^2}{|1-x^2|}$.

As an aside, it's definitely baffling that a behemoth program like SAGE is outdone in this respect by a one-floppy-disk, antique program called DERIVE.

As another aside, I still have to find a meaningful use for the instruction simplify(). Can someone provide me an expression that is actually simplified by simplify()?

simplification errors in simple expressions

I'm currently testing the possibilities of SAGE as a teaching aid in a high school math course (in Belgium). I stumbled upon this:

• When evaluating x/sqrt(x^2), SAGE answers $\frac{x}{|x|}$, as it should. Appending a .simpify()-instruction to the input does not change anything.
• However, ((1-x^2)/sqrt(1-2*x^2+x^4)).simplify_full() evaluates to $-1$, in stead of $\frac{1-x^2}{|1-x^2|}$.

As an aside, it's definitely baffling that a behemoth program like SAGE is outdone in this respect by a one-floppy-disk, antique program called DERIVE.

As another aside, I still have to find a meaningful use for the instruction simplify(). Can someone provide me an expression that is actually simplified by simplify()?

Note added: I'm not sure I'm satisfied with mr. Bateman's answer (and I definitely disagree that defining sqrt(x^2)=|x| - for real x - entails +1=-1). But what I really want to know is this: is there a SAGE object that represents (reliably) the positive square root of a positive real number x? (Surely a quantity that is not without interest.) And how do I define it in SAGE?

 3 Fateman not Bateman kcrisman 11972 ●37 ●124 ●241

simplification errors in simple expressions

I'm currently testing the possibilities of SAGE as a teaching aid in a high school math course (in Belgium). I stumbled upon this:

• When evaluating x/sqrt(x^2), SAGE answers $\frac{x}{|x|}$, as it should. Appending a .simpify()-instruction to the input does not change anything.
• However, ((1-x^2)/sqrt(1-2*x^2+x^4)).simplify_full() evaluates to $-1$, in stead of $\frac{1-x^2}{|1-x^2|}$.

As an aside, it's definitely baffling that a behemoth program like SAGE is outdone in this respect by a one-floppy-disk, antique program called DERIVE.

As another aside, I still have to find a meaningful use for the instruction simplify(). Can someone provide me an expression that is actually simplified by simplify()?

Note added: I'm not sure I'm satisfied with mr. Bateman's Fateman's answer (and I definitely disagree that defining sqrt(x^2)=|x| - for real x - entails +1=-1). But what I really want to know is this: is there a SAGE object that represents (reliably) the positive square root of a positive real number x? (Surely a quantity that is not without interest.) And how do I define it in SAGE?

 4 retagged tmonteil 23043 ●25 ●165 ●421 http://wiki.sagemath.o...

simplification errors in simple expressions

I'm currently testing the possibilities of SAGE as a teaching aid in a high school math course (in Belgium). I stumbled upon this:

• When evaluating x/sqrt(x^2), SAGE answers $\frac{x}{|x|}$, as it should. Appending a .simpify()-instruction to the input does not change anything.
• However, ((1-x^2)/sqrt(1-2*x^2+x^4)).simplify_full() evaluates to $-1$, in stead of $\frac{1-x^2}{|1-x^2|}$.

As an aside, it's definitely baffling that a behemoth program like SAGE is outdone in this respect by a one-floppy-disk, antique program called DERIVE.

As another aside, I still have to find a meaningful use for the instruction simplify(). Can someone provide me an expression that is actually simplified by simplify()?

Note added: I'm not sure I'm satisfied with mr. Fateman's answer (and I definitely disagree that defining sqrt(x^2)=|x| - for real x - entails +1=-1). But what I really want to know is this: is there a SAGE object that represents (reliably) the positive square root of a positive real number x? (Surely a quantity that is not without interest.) And how do I define it in SAGE?

 5 retagged tmonteil 23043 ●25 ●165 ●421 http://wiki.sagemath.o...

simplification errors in simple expressions

I'm currently testing the possibilities of SAGE as a teaching aid in a high school math course (in Belgium). I stumbled upon this:

• When evaluating x/sqrt(x^2), SAGE answers $\frac{x}{|x|}$, as it should. Appending a .simpify()-instruction to the input does not change anything.
• However, ((1-x^2)/sqrt(1-2*x^2+x^4)).simplify_full() evaluates to $-1$, in stead of $\frac{1-x^2}{|1-x^2|}$.

As an aside, it's definitely baffling that a behemoth program like SAGE is outdone in this respect by a one-floppy-disk, antique program called DERIVE.

As another aside, I still have to find a meaningful use for the instruction simplify(). Can someone provide me an expression that is actually simplified by simplify()?

Note added: I'm not sure I'm satisfied with mr. Fateman's answer (and I definitely disagree that defining sqrt(x^2)=|x| - for real x - entails +1=-1). But what I really want to know is this: is there a SAGE object that represents (reliably) the positive square root of a positive real number x? (Surely a quantity that is not without interest.) And how do I define it in SAGE?

 6 retagged tmonteil 23043 ●25 ●165 ●421 http://wiki.sagemath.o...

simplification errors in simple expressions

I'm currently testing the possibilities of SAGE as a teaching aid in a high school math course (in Belgium). I stumbled upon this:

• When evaluating x/sqrt(x^2), SAGE answers $\frac{x}{|x|}$, as it should. Appending a .simpify()-instruction to the input does not change anything.
• However, ((1-x^2)/sqrt(1-2*x^2+x^4)).simplify_full() evaluates to $-1$, in stead of $\frac{1-x^2}{|1-x^2|}$.

As an aside, it's definitely baffling that a behemoth program like SAGE is outdone in this respect by a one-floppy-disk, antique program called DERIVE.

As another aside, I still have to find a meaningful use for the instruction simplify(). Can someone provide me an expression that is actually simplified by simplify()?

Note added: I'm not sure I'm satisfied with mr. Fateman's answer (and I definitely disagree that defining sqrt(x^2)=|x| - for real x - entails +1=-1). But what I really want to know is this: is there a SAGE object that represents (reliably) the positive square root of a positive real number x? (Surely a quantity that is not without interest.) And how do I define it in SAGE?

 7 retagged tmonteil 23043 ●25 ●165 ●421 http://wiki.sagemath.o...

simplification errors in simple expressions

I'm currently testing the possibilities of SAGE as a teaching aid in a high school math course (in Belgium). I stumbled upon this:

• When evaluating x/sqrt(x^2), SAGE answers $\frac{x}{|x|}$, as it should. Appending a .simpify()-instruction to the input does not change anything.
• However, ((1-x^2)/sqrt(1-2*x^2+x^4)).simplify_full() evaluates to $-1$, in stead of $\frac{1-x^2}{|1-x^2|}$.

As an aside, it's definitely baffling that a behemoth program like SAGE is outdone in this respect by a one-floppy-disk, antique program called DERIVE.

As another aside, I still have to find a meaningful use for the instruction simplify(). Can someone provide me an expression that is actually simplified by simplify()?

Note added: I'm not sure I'm satisfied with mr. Fateman's answer (and I definitely disagree that defining sqrt(x^2)=|x| - for real x - entails +1=-1). But what I really want to know is this: is there a SAGE object that represents (reliably) the positive square root of a positive real number x? (Surely a quantity that is not without interest.) And how do I define it in SAGE?