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Question: Why is simplify ineffective with these combined assumptions?

Question:Why is simplify ineffective with these combined assumptions?

C_R 2847 Maple
simplify assumptions arctan duplicate-question
May 15 2022
2

The expression

f := arctan(y, x)+arctan(-y, x)

arctan(y, x)+arctan(-y, x)

 (1)

simplifies to zero in the real range if y=0 is excluded.

x < 0, y::real, y <> 0; `assuming`([simplify(f), is(f = 0)], [%])

0, true

 (2)

x >= 0, y::real, y <> 0; `assuming`([simplify(f), is(f = 0)], [%])

0, true

 (3)

Combining the above assumptions as attempted bellow does not simplify to zero

x::real, y::real, y <> 0; `assuming`([simplify(f), is(f = 0)], [%])

arctan(y, x)+arctan(-y, x), FAIL

 (4)

`or`(x < 0, x >= 0), y::real, y <> 0; `assuming`([simplify(f), is(f = 0)], [%])

arctan(y, x)+arctan(-y, x), FAIL

 (5)

Or(x < 0, x >= 0), y::real, y <> 0; `assuming`([simplify(f), is(f = 0)], [%])

arctan(y, x)+arctan(-y, x), FAIL

 (6)

`and`(-infinity <= x, x <= infinity), y::real, y <> 0; `assuming`([simplify(f), is(f = 0)], [%])

arctan(y, x)+arctan(-y, x), FAIL

 (7)

interface(version)

`Standard Worksheet Interface, Maple 2022.0, Windows 10, March 8 2022 Build ID 1599809`

 (8)

 

  

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