Words for diagonal directions

I have seen them being referred to as positive diagonal (forward slash, / ) and negative diagonal (backslash, \ ), basically in reference to their slope as seen in a standard euclidean axial system.

In a mathematical setting, I feel those terms might be more intuitive than names of accents most speakers of English are not directly familiar with.

As mentioned in a comment, I probably picked up this usage from sodoku. It is used regularly on the cracking the cryptic Youtube channel. Logic masters Germany uses this terminology as well:

Digits cannot repeat along the positive diagonal.

One idea is to call them according to their attitude from left to right, that is, an inclining diagonal when going from bottom to top and a declining diagonal when going from top to bottom.

For example, these quilting directions by Linda Ambrosini ("Pixie Sticks," Hoffman Fabrics) make use of the inclining cut and inclining diagonal to describe a cut going from bottom left to top right and the declining cut and diagonal for the other case. Then an explanation of Hanidoku, a hexagonal Sudoku variant, uses inclining diagonal and descending diagonal to describe lines of hexagons.

You could also use rising and falling diagonal, which are the names of the Unicode characters ⟋ and ⟍, respectively (Compart 1, 2). In both cases, you rely on an English reader's tendency to read from left to right and thus to perceive a line as rising or falling based on its behavior going from left to right.

It's a bit off the wall, but could you possibly rotate your problem to dividing a diamond into two triangles? Then you can refer to the lines as vertical and horizontal, and avoid any confusion.

Given the standard (and very widespread) road signs for hills such as that below which is for an uphill gradient.

I would suggest that either Ascending/Descending or Up/down slant.

Of course in a formal paper you could always mention, or illustrate, the words that you decide to use either in an introductory section or at the first usage.