# Changes between Version 4 and Version 31 of Ticket #7660

Ignore:
Timestamp:
02/12/15 08:07:22 (7 years ago)
Comment:

Let's start this fresh. To summarize, what's wanted is the following:

equations:

• `(a==b) +-*/ c` same as:
• `(a==b).add_to_both_sides(c)`
• `(a==b).subtract_from_both_sides(c)`
• `(a==b).multiply_both_sides(c)`
• `(a==b).divide_both_sides(c)`
• `False` if `*/0`
• `(a==b)^c` --> `a^c == b^c`
• `f(a==b)` --> `f(a==b)`

relations:

• `(a<b) +- c` same as:
• `(a<b).add_to_both_sides(c)`
• `(a<b).subtract_from_both_sides(c)`
• `(a<b) */ c` same as:
• `a*/c > b*/c` for `c` real and negative, or if `c` is assumed negative
• `a*/c < b*/c` for `c` real and positive, or if `c` is assumed positive
• `False` if `c=0`
• `(a<b)^c` --> `(a<b)^c`
• `f(a<b)` --> `f(a<b)`

Question: Real or: if coerced to the reals successfully? A followup extension would be like Maxima's ineq package, i.e., ask before doing a sign switch.

Unmodified
Removed
Modified
• ## Ticket #7660

• Property Status changed from `new` to `needs_work`
• Property Authors changed from to `Burcin Erocal, Ralf Stephan`
• Property Summary changed from `arithmetic with inequalities confusing` to `arithmetic with equations and inequalities confusing`
• Property Branch changed from to `u/rws/ticket/7660`
• Property Milestone changed from `sage-5.11` to `sage-6.4`
• Property Keywords inequality solver maxima added
• Property Commit changed from to `30cc86077172f9e57c6b5df06b40158e17e2320d`
• ## Ticket #7660 – Description

 v4 Equations and relations should behave like this: equations: * `(a==b) +-*/ c` same as: - `(a==b).add_to_both_sides(c)` - `(a==b).subtract_from_both_sides(c)` - `(a==b).multiply_both_sides(c)` - `(a==b).divide_both_sides(c)` - `False` if `*/0` * `(a==b)^c` --> `a^c == b^c` * `f(a==b)` --> `f(a==b)` relations: * `(a b*/c` for `c` real and negative, or if `c` is assumed negative - `a*/c < b*/c` for `c` real and positive, or if `c` is assumed positive - `False` if `c=0` * `(a `(a `f(a