Elementary math

This page contains some tests for the MathML elementary math elements. These are rendered via the 'elemMath.js' polyfill.

mstack examples from MathML spec (some general examples)

1. Simple addition with operator on the left

   Image	MathML
   	$$424+33$$

2. Simple addition with operator on the right

   Image	MathML
   	$$123456+579$$

3. Two examples showing carries and crossouts

   Image	MathML
   	$$212\mathrm{2,327}-\mathrm{1,156}\mathrm{1,171}$$
   	$$21\mathrm{2,327}-\mathrm{1,156}\mathrm{1,171}$$

4. Carries and crossouts, but with multiple digits in carry and underlined

   Image	MathML
   	$$\underline{10}52-745$$

5. Simple multiplication (uses msgroup)

   Image	MathML
   	$$123\times <!--MULTIPLICATION\; SIGN-->321123246369$$

6. This example has multiple rows of carries. It also (somewhat artificially) includes commas (",") as digit separators. The encoding includes these separators in the spacing attribute value.

   Image	MathML
   	$$1111\mathrm{1,234}\times <!--MULTIPLICATION\; SIGN-->\mathrm{4,321}11111\mathrm{1,234}\mathrm{24,68}\mathrm{370,2}\mathrm{4,936}\mathrm{5,332,114}$$

7. Repeating decimals (line over 3): $$0.3333$$
8. Repeating decimals (line over fractional part): $$0.142857$$
9. Repeating decimals (line under fractional part): $$0.142857$$
10. Repeating decimals (dots over start and end of fractional part): $$..0.142857$$

mstack

Test with different number of args

1. mstack with no elements (should be empty, no console warnings): $$$$
2. mstack with a single number (should just be a number): $$123$$
3. 2 arguments (simple stack of numbers): $$123456$$

Test with different attr args/values

align

Not implemented

stackalign (alignment of stack of elements

1. left $$2123.4456.018+2579.418$$
2. center $$2123.4456.018+2579.418$$
3. right $$2123.4456.018+2579.418$$
4. decimal $$2123.4456.018+2579.418$$
5. decimal (default value) $$2123.4456.018+2579.418$$
6. decimal (default value, using inherited value set by mstyle) $$\mathrm{2123,}\mathrm{456,018}+\mathrm{2579,418}$$

charalign (alignment of character in a column)

1. left $$12\mathrm{wide}1$$
2. center $$12\mathrm{wide}1$$
3. right $$12\mathrm{wide}1$$
4. default (right) $$12\mathrm{wide}1$$

charspacing

1. loose $$432+33$$
2. medium $$432+33$$
3. tight $$432+33$$
4. value (1em -- really wide) $$432+33$$
5. tight with a none value $$4321+33$$

msgroup tests

Test with different number of args

1. msgroup with no elements (should be empty, no console warnings): $$$$
2. msgroup with a single number (position=2, shift=1 -- visually not much but two empty columns on right): $$123$$
3. msgroup with 2 arguments (position=-1, shift=2 -- visually '1's should align): $$123321$$
4. Nested msgroups (position=-1, shift=2, with position=-1, shift=1 nested inside (rows 4-6)-- visually all digits should align): $$1232343455674563450123$$

Test with different attr args/values

position

1. two msgroups (position=1, position=-1) -- the '3's should align: $$123345$$
2. two msgroups (1st two lines position=1, last two lines position=-1) -- the '3's should align. $$123123345345$$

shift

msrow tests

Test with different number of args

1. $$$$
2. msrow with a single number -- visually not much: $$123$$
3. msrow with 3 arguments -- the two decimal numbers should align: $$123.45|456123.45$$

Test with different attr args/values

position

1. mrow with no elements (position=2) -- should be empty, no console warnings: $$$$
2. msrow with a single number (position="-2") -- visually not much (should be two blank cells on left): $$123$$
3. msrows (position=1, position=-1) -- the "3"s should align: $$123345$$

mscarries tests

Test with different number of args

1. mscarries with no elements (position=2) -- should see just "123", no padding, no console warnings: $$123$$
2. mscarries with no elements and no following line (position=2) -- should not see anything, no console warnings: $$$$
3. mscarries with one child and no following line (position=2) -- should see a small 9, no console warnings: $$9$$
4. mscarries with two children, should see 8 over 2, 9 over the 3: $$89123$$
5. mscarries with two children (position=2), should see 1 over empty space, 9 over the 2: $$129$$
6. two rows of mscarries over each other, should see carry "1" over carry "2" over "9": $$12789$$
7. three rows of mscarries over each other, should see carry "1" over carry "2" over carry "3" over "9": $$123789$$
8. two rows of numbers with a carry between them (3"s should align, with middle one small, not crash together or crash into line): $$1233543$$

Test with different attr args/values

position

1. mscarries with single child (position=-1), should see 9 one column to the right of 3: $$9123$$
2. mscarries with single child (position=1), should see 9 over 2: $$9123$$
3. mscarries with single child and no position give should see 9 over 1: $$9123$$

location

1. "w": 8 and 9 should be before 2 and 3 respectivly $$89123$$
2. "nw": 8 and 9 should be pre-superscripts before 2 and 3 respectivly $$89123$$
3. "n": 8 and 9 should be above 2 and 3 respectivly $$89123$$
4. "ne": 8 and 9 should be superscripts to 2 and 3 respectivly $$89123$$
5. "e": 8 and 9 should be after 2 and 3 respectivly $$89123$$
6. "se": 8 and 9 should be subscripts to 2 and 3 respectivly $$89123$$
7. "s": 8 and 9 should be below 2 and 3 respectivly $$89123$$
8. "sw": 8 and 9 should be presubscripts before 2 and 3 respectivly $$89123$$
9. default ("n"): 8 and 9 should be above 2 and 3 respectivly $$89123$$

crossout

1. No cross out ("none") (carry "n": 9 should be above 3) $$9123$$
2. Crossout is updiagonalstrike (carry "ne": 9 should be superscript to 3) $$9123$$
3. Crossout is downdiagonalstrike (carry "nw": 9 should be superscript to 3) $$9123$$
4. Cross out is verticalstrike (carry "n": 9 should be above 3) $$9123$$
5. Crossout is horizontalstrike (carry "ne": 9 should be superscript to 3) $$9123$$
6. Crossout is both downdiagonalstrike and updiagonalstrike (carry "nw": 9 should be superscript to 3) $$9123$$
7. Crossout is all four (carry "n, position=1": 9 should be above the 2) $$9123$$
8. Crossout is both downdiagonalstrike (twice) and updiagonalstrike (carry "nw": 9 should be superscript to 3) -- lots of extra spaces in attr value $$9123$$

scriptsizemultiplier

1. .4 -- should be smaller than normal (compare to second line of carries) $$891234589123$$
2. 1.5 -- should be bigger than normal (compare to second line of carries) and overflow into each other $$891234589123$$
3. .4 -- should be smaller than normal (value inherited from mstyle). Both rows of carries should be small. $$891234589123$$

mscarry tests

Test with different number of args

1. mscarry with no child -- should see no change (just 123): $$\mathrm{}123$$
2. mscarry with single child and no position give should see 9 over 3: $$9123$$
3. mscarry with multiple digits over "2" -- should overflow to other columns and not change spacing: $$789123$$

Test with different attr args/values

location

1. mscarry with location starting a "w" (on left) ending with "sw" and finally default inheritance of "n" over 9; nothing should be over the "+": $$000000000+123456789$$
2. mscarry with location starting a "w" (on left) ending with "sw" and finally default inheritance of "nw" over 9; nothing should be over the "+": $$000000000+123456789$$

crossout

1. mscarry with crossout starting at "none", "updiagonalstrike", "downdiagonalstrike", "verticalstrike", "horizontalstrike", with the default of diag up/down over the "9": $$+56789$$

msline tests

Test with different number of args

1. only a msline (length=3) -- should display as a line, perhaps somewhat short due to cells having a small width: $$$$
2. msline first line (position="1" length="2") -- should be above 1 and 2: $$123$$

Test with different attr args/values

position

1. msline (position=1, length unspecified) -- should draw line under all digits: $$123$$
2. msline (position=1, length=1) -- should draw line under "2": $$123$$
3. msline (position=4, length=1) -- should draw line before "1": $$123$$
4. msline (position=-1, length=1) -- should draw line after "3": $$123$$

length

1. Both lines should be all the way across (default value) $$123\times <!--MULTIPLICATION\; SIGN-->321123246369$$
2. Both lines should be all the way across (length=0) $$123\times <!--MULTIPLICATION\; SIGN-->321123246369$$
3. First line only to "×" (length=4); second only under 369 (length=3, position=2) $$123\times <!--MULTIPLICATION\; SIGN-->321123246369$$
4. line extends beyond number one column on each side (length=5, position=-1) $$123$$

leftoverhang

Not implemented

rightoverhang

Not implemented

mslinethickness

1. thin $$123$$
2. medium $$123$$
3. thick $$123$$
4. default (medium) $$123$$
5. 3ex (very fat) $$123$$

inherited value of mathcolor

1. the number and line should be gray $$123$$
2. mstyle inside of mstyle -- numbers should be gray, the second should be a fat blue line $$123$$

mlongdiv

Long division examples from MathML spec (the polyfill supports a "decimalpoint" attr on "mlongdiv"/"mstack", which is not part of MathML 3; see this issue for why)

longdivstyle	lefttop	stackedrightright	mediumstackedrightright	shortstackedrightright	righttop
Image from spec
Polyfill rendering	$$3435.313061210916151.091$$	$$3\mathrm{435,3}1306121091615\mathrm{1,0}91$$

longdivstyle	left/\right	left)(right	:right=right	stackedleftleft	stackedleftlinetop
Image from spec
Polyfill rendering					$$\mathrm{٣<!--ARABIC-INDIC\; DIGIT\; THREE-->}\mathrm{٤<!--ARABIC-INDIC\; DIGIT\; FOUR-->٣<!--ARABIC-INDIC\; DIGIT\; THREE-->٥<!--ARABIC-INDIC\; DIGIT\; FIVE-->٫<!--ARABIC\; DECIMAL\; SEPARATOR-->٣<!--ARABIC-INDIC\; DIGIT\; THREE-->}\mathrm{١<!--ARABIC-INDIC\; DIGIT\; ONE-->٣<!--ARABIC-INDIC\; DIGIT\; THREE-->٠<!--ARABIC-INDIC\; DIGIT\; ZERO-->٦<!--ARABIC-INDIC\; DIGIT\; SIX-->}\mathrm{١<!--ARABIC-INDIC\; DIGIT\; ONE-->٢<!--ARABIC-INDIC\; DIGIT\; TWO-->}\mathrm{١<!--ARABIC-INDIC\; DIGIT\; ONE-->٠<!--ARABIC-INDIC\; DIGIT\; ZERO-->}\mathrm{٩<!--ARABIC-INDIC\; DIGIT\; NINE-->}\mathrm{١<!--ARABIC-INDIC\; DIGIT\; ONE-->٦<!--ARABIC-INDIC\; DIGIT\; SIX-->}\mathrm{١<!--ARABIC-INDIC\; DIGIT\; ONE-->٥<!--ARABIC-INDIC\; DIGIT\; FIVE-->}\mathrm{١<!--ARABIC-INDIC\; DIGIT\; ONE-->٫<!--ARABIC\; DECIMAL\; SEPARATOR-->٠<!--ARABIC-INDIC\; DIGIT\; ZERO-->}\mathrm{٩<!--ARABIC-INDIC\; DIGIT\; NINE-->}\mathrm{١<!--ARABIC-INDIC\; DIGIT\; ONE-->}$$

Long divsion with too few arguments

No arguments

One argument

1. $$11.1$$

Two arguments

1. $$11.122.2$$

Three arguments

1. $$11.122.233.3$$