Dot Products and Vector (Cross) Products Are Not Distinguished in Speech

[NV-Codes]

MathCAT Version

MathCAT-0.6.6 (NVDA Add-On)

Description of Issue

MathCAT's speech verbalizes both the dot multiplication symbol and the cross multiplication symbol as "times," as well as some implicit multiplication (multiplication implied by adjacency). An issue arises in calculus and physics when the dot and cross symbols mean different types of vector operations, and failing to disambiguate the type of multiplication greatly hinders proper understanding of math content.

For instance, the dot product of vector A and vector B ($\vec{A} \cdot \vec{B}$) and the cross product between vector A and vector B ($\vec{A} \times \vec{B}$) are both verbalized as "vector cap A times vector cap B."

Proposed Solution

A checkbox in MathCAT's "Speech" settings could allow the user to toggle disambiguation of dot and cross multiplication.

• Verbalize dot and cross multiplication differently
• Verbalize dot and cross multiplication differently

Simply verbalizing "dot" and "cross" for the respective symbols when the option is checked should suffice, as that seems clear and concise.

[NSoiffer]

Thanks for your suggestion. I'm not keen on adding lots of "little" tweaks in the UI. The more that get added, the harder it becomes to find any individual feature. Also, most people never change from the defaults.

What might work is trying to detect that the operands are vectors. The check could be that the operands are either bold letters or letters with a right arrow or harpoon above. In those cases say either "dot" or "cross". Would that solve this issue for you?

[NV-Codes]

Yes, I think that would solve the issue, as long as letters with hats are included as well. For example, $\hat{x} \times \hat{y} = \hat{z}$ is a relation of unit vectors in a right-handed Cartesian coordinate system.

[NV-Codes]

It would also be important to consider formulas like the following:

Magnetic Flux through a Surface:

$$\Phi_B = \oint \mathbf B \cdot d \mathbf A$$

Magnetic Field Produced by a Current-Carrying Loop ($C_2$):

$$\mathbf B_2 (\mathbf r_1) = \frac{\mu_0}{4\pi} \oint \limits_{C_2} I_2 d\mathbf s_2 \times \frac{\mathbf r_1 - \mathbf r_2}{|\mathbf r_1 - \mathbf r_2|^3}$$

Force on Loop 1 ($C_1$) by Loop 2 ($C_2$):

$$\mathbf F_1 = -\frac{\mu_0}{4\pi} \oint \limits_{C_1} I_1 d \mathbf s_1 \cdot \oint \limits_{C_2} I_2 d \mathbf s_2 \frac{\mathbf r_1 - \mathbf r_2}{|\mathbf r_1 - \mathbf r_2|^3}$$

Takeaway

The operands could be differential vectors, vector fractions, or even integrals that represent vector quantities. Maybe MathCAT could verbalize "dot" and "cross" within all math content that includes any vector.