Why is $(1-t)^2 == (t-1)^2$ in SageMath?

Question

This is really odd, not much to say about it.

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│ SageMath version 8.5, Release Date: 2018-12-22                     │
│ Using Python 2.7.15. Type "help()" for help.                       │
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Are you sure this question wouldn't be better answered in another SE? — , Jan 19 '19 at 04:06
That depends on what type of answer you're looking for. If you're looking for a reason as to why Python respond and return this result, Stack Overflow might be a better choice. If you want a mathematical explanation, then I would suggest leaving the question on this site and trying to see if someone knows the answer — , Jan 19 '19 at 04:11
What is "odd" about this? Do you have reason to doubt the result? What result did you expect and why? — JMoravitz, Jan 19 '19 at 04:15

score 1 · Accepted Answer · answered Jan 19 '19 at 04:11

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This is just basic algebra, namely laws of exponents:

$(t-1)^2 = (-1(1-t))^2= (-1)^2(1-t)^2 = (1-t)^2$

answered Jan 19 '19 at 04:11

Randall

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should have paid attention in elementary school – Louis Hong Jan 19 '19 at 04:16
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To really see it, let $t=3$. This says $2^2= (-2)^2$. Well, yeah. – Randall Jan 19 '19 at 04:16
@LouisHong You don't learn this in elementary, you learn this in algebra, guess you didn't pay attention in there either haha – Some Guy Mar 19 '21 at 16:25

score 1 · Answer 2 · answered Jan 19 '19 at 04:40

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Forget $1-t$. Instead, think $T$. Is it so surprising/odd that $$(T)^2 = (-T)^2$$ ?

Alternatively we can expand them:

$$(1-t)(1-t)=(1)(1) +(2)(1)(-t)+(-t)(-t)=1-2t+t^2$$

$$(t-1)(t-1)=(t)(t)+2(-1)(t)+(-1)(-1)=t^2-2t+1$$

answered Jan 19 '19 at 04:40

Rhys Hughes

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Why is $(1-t)^2 == (t-1)^2$ in SageMath?

2 Answers2