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MathML Accessibility in Mozilla

This table below provides a list of MathML constructions and how they are read in Mozilla applications for various platforms:

  • Windows: MathML support is provided by NVDA, which actually delegates math reading to the proprietary MathPlayer plugin. We started exposing generic accessible objects for MathML in bug 920547 and so these can be retrieved by NVDA starting with Gecko 27.0 (Firefox 27.0 / Thunderbird 27.0 / SeaMonkey 2.24). Mozilla and NVDA developers essentially do not have control on how mathematical formulas are read, please contact Design Science for any inquiries.
  • Mac: MathML support is provided by VoiceOver. In bug 1175269 and bug 1001641, we relied on the WebKit's NSAccessibility MathML tree to expose the main constructions. Hence basic support is available in Gecko 41.0 (Firefox 41.0 / Thunderbird 41.0 / SeaMonkey 2.38) and we are still trying to keep in sync with WebKit/VoiceOver. Note that VoiceOver is proprietary so we do not have control on Improvements to MathML accessibility in VoiceOver.
  • Linux: MathML support is provided by the development version of Orca. We try to keep in sync with WebKit/ATK/Orca developments. At the moment, it is recommended to use a Nightly build to ensure that the accessible tree expected by Orca is correctly exposed.
  • AccessFu: MathML support in Android and Firefox OS is currently being implemented in our AccessFu module and a patch is available on bug 1163374. The table gives the output in mode "utterance" and description spoken last. Note that this is still very experimental.
MathML Windows Mac Linux AccessFu
Diagonal of a regular pentagon Video Video Video /
x+2 __________

plus 

 
__________
x+2 x plus 2 x + y
ab __________
 
a
over 

 
__________
fraction start, a over b, end of fraction fraction start. a over b. fraction end. a numerator b denominator fraction
ab\frac a b        
ab __________
 
a
over 

 
__________
fraction start, a over b, end of fraction. See WebKit's bug 146454 fraction without bar, start. a over b. fraction end. a numerator b denominator fraction without bar
ab __________
a
sub 

 
__________
a, subscript b a. subscript b

a base b subscript scripted

ab __________
a
raised to the 

 
__________
a, superscript b a. superscript b

a base b superscript scripted

abc __________
a
sub 

to the 
c
 
 
__________
a, subscript b, superscript c a. subscript b superscript c a base b subscript c superscript scripted
ab __________
a
with 

below 
 
__________
a. See WebKit's bug 146407 a. underscript b a base b underscript scripted
ab __________
a
with 

above 
 
__________
a, with b underneath. See WebKit's bug 146407 a. overscript b a base b overscript scripted
abc __________
a
with 

below and with 

above 
 
__________
a, with c underneath. See WebKit's bug 146407 a. underscript b overscript c

a base b underscript c overscript scripted

a __________
the square root of 
a
 
__________
square root of a, end of root square root of a. root end. a square root
abc __________
the square root of the quantity 
a


end root 
 
__________
square root of a, end of root. See WebKit's bug 146452 square root of a b c. root end.

a b c square root

a2 __________
the 
second 
root of 
a
 
__________
square root of a, end of root square root of a. root end.

a base root index root

a3 __________
the 
third 
root of 
a
 
__________
cube root of a, end of root cube root of a. root end. a base 3 root index root
a3+4 __________
the 

plus 

root of 
a
 
__________
3 + 4 root of a, end of root 3 plus 4 root of a. root end.

a base 3+4 root index root

a34 __________
the  
3 over 

root of 
a
 
__________
fraction start, 3 over 4, end of fraction root of a, end of root fraction start. 3 over 4. fraction end. root of a. root end. a base 3 numerator 4 denominator root-index fraction
ab __________
the 
the square root of 

root of 
a
 
__________
square root of b, end of root root of a, end of root square root of b. root end. root of a. root end. a base b square root root-index root
ab __________
the square root of the quantity  
a
over 

end root 
 
__________
square root of fraction start, a over b, end of fraction, end of root square root of fraction start. a over b. fraction end. root end. a numerator b denominator fraction square root
ab3 __________
the 
third 
root of 
 
a
over 

end root 
 
__________
cube root of fraction start a over b, end of fraction, end of root cube root of fraction start. a over b. fraction end. root end. a numerator b denominator fraction base 3 root-index root
abc+d __________
the 

plus 

root of 
 
a
over 

end root 
 
__________
c + d root of fraction start, a over b, end of fraction, end of root c plus d root of fraction start. a over b. fraction end. root end. a numerator b denominator fraction base c + d root-index root
ab __________
the 
b
root of 
a
 
__________
b root of a, end of root b root of a. root end.

a base b root index root

abcdef __________
table with 2 rows and 3 columns 
row 1 
column 1 
a
column 2 

column 3 

row 2 
column 1 

column 2 

column 3 

end table 
 
__________
Table start, Row 1, Column 1, a, Row 1, Column 2, b, Row 1, Column 3, c, Row 2, Column 1, d, Row 2, Column 2, e, Row 2, Column 3, f, table end

math table with 2 rows 3 columns. row 1. a. b. c. row 2. d. e. f. table end.

a column 1 row 1 b column 2 c column 3 d column 1 row 2 e column 2 f column 3 math table with 3 columns and 2 rows

abcde __________
multi-scripts 
with base 
a
and 1 prescript and 1 post-script 
pre-scripts 
lower 

upper 

post-scripts 
lower 

upper 

end multi-scripts 
 
__________
Not supported yet. See bug 1176983 and WebKit's bug 146454 a. pre-subscript d pre-superscript e subscript b.superscript c

a base b subscript c superscript d presubscript e presuperscript scripted

a b c d e __________
multi-scripts 
with base 
a
and 2 post-scripts 
lower 

upper 

lower 

upper 

end multi-scripts 
 
__________
Not supported yet. See bug 1176983 and WebKit's bug 146454 a. subscript b superscript c subscript d superscript e a base b subscript c superscript d subscript e superscript scripted
a b c d e __________
multi-scripts 
with base 
a
and 2 prescripts and 0 post-scripts 
pre-scripts 
lower 

upper 

lower 

upper 

post-scripts 
 
__________
Not supported yet. See bug 1176983 and WebKit's bug 146454 a. pre-subscript b pre-superscript c pre-subscript d pre-superscript e a base b presubscript c presuperscript d presubscript e presuperscript scripted
a b c d e f g __________ 
multi-scripts 
with base 
a
and 2 prescripts and 2 post-scripts 
pre-scripts 
lower 

upper 

upper 

post-scripts 
lower 

lower 

upper 

end multi-scripts 
 
__________
Not supported yet. See bug 1176983 and WebKit's bug 146454 a. pre-subscript e pre-superscript f pre-superscript g subscript b subscript c superscript d a base b subscript c subscript d superscript e presubscript f presuperscript g presuperscript scripted
x+y __________
long division symbol enclosing 

plus 

end symbol 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a long division sign

x + y long division enclosed

 

x+y __________
long division symbol enclosing 

plus 

end symbol 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a long division sign

x + y long division enclosed

x+y __________
actuarial symbol enclosing 

plus 

end symbol 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: an actuarial symbol

x + y actuarial enclosed

x+y __________

plus 

 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a phasor angle

 

x + y phasor angle enclosed

x+y __________
the square root of the quantity 

plus 

end root 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a radical x + y radical enclosed
x+y __________
begin box 

plus 

end box 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a box x + y box enclosed
x+y __________
begin rounded box 

plus 

end rounded box 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a rounded box x + y rounded box enclosed
x+y __________
begin circle 

plus 

end circle 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a circle x + y circle enclosed
x+y __________
line left of 

plus 

end line 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a line on the left x + y left enclosed
x+y __________
line right of 

plus 

end line 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a line on the right x + y right enclosed
x+y __________
line above 

plus 

end line 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a line at the top x + y top enclosed
x+y __________
line below 

plus 

end line 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a line at the bottom x + y bottom enclosed
x+y __________

plus 

 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a line on the left and a line on the right x + y right left enclosed
x+y __________

plus 

 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a line at the bottom, a line on the left, a line on the right, and, a line at the top x + y bottom top right enclosed
x+y __________
cross out enclosing 

plus 

end crossout 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: an up diagonal strike x + y up diagonal strike enclosed
x+y __________
cross out enclosing 

plus 

end crossout 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a down diagonal strike x + y down diagonal strike enclosed
x+y __________
cross out enclosing 

plus 

end crossout 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a vertical strike x + y up vertical strike enclosed
x+y __________
cross out enclosing 

plus 

end crossout 
 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: a horizontal strike x + y horizontal strike enclosed
x+y __________

plus 

 
__________
Not supported. See WebKit's bug 146543. x plus y Enclosed by: an arabic factorial symbol x + y up madruwb enclosed
abcd e __________
open 
a
comma 

comma 

comma 

comma 

close 
 
__________
Not supported. See bug 1176970 ; Safari+VoiceOver reads "(, abcde, )". left paren. a comma. b comma. comma. d comma. e. right paren Not supported.
abcd e __________
the set 
a








end set 
 
__________
Not supported. See bug 1176970 ; Safari+VoiceOver reads "{, abcde, }". left brace. a semicolon. b semicolon. c semicolon. d semicolon. e. right brace Not supported.
abcde __________
the set 
a




comma 

comma 

end set 
 
__________
Not supported. See bug 1176970 ; Safari+VoiceOver reads "{, abcde, }". left brace. a semicolon. b semicolon. c comma. d comma. e. right brace Not supported.
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz     Not exposed to Orca. See bug 1182469  
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz     Not exposed to Orca. See bug 1182469  
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz     Not exposed to Orca. See bug 1182469  
(x≪̸y)(X⊂⃒Y)        
Torture Test 1: x 2 y 2 __________

squared 

squared 
__________
x squared y squared x. superscript 2. y. superscript 2. x base 2 superscript scripted y base 2 superscript scripted
Torture Test 2: F 3 2 __________
multi-scripts 
with base 
cap f 
and 1 prescript and 1 post-script 
pre-scripts 
lower 

post-scripts 
lower 

end multi-scripts 
__________
Not supported yet. See bug 1176983 and WebKit's bug 146454 F. pre-subscript 2 subscript 3 F base 3 subscript 2 presubscript scripted
Torture Test 3: x + y 2 k + 1 __________
fraction 

plus 

squared 
over 

plus 

end fraction 
__________
fraction start, x + y squared over k + 1, end of fraction fraction start. x plus y. superscript 2. over k plus 1. fraction end. x + y base 2 superscript scripted numerator k + 1 denominator fraction
Torture Test 4: x + y 2 k + 1 __________

plus 
y raised to the 
fraction 

over 

plus 

end fraction 
power 
__________
x + y, superscript fraction start, 2 over k + 1, end of fraction x plus y. superscript fraction start. 2 over k plus 1. fraction end. x + y base 2 numerator k + 1 denominator fraction superscript scripted
Torture Test 5: a b / 2 __________
fraction 
a
over 

divided by 

end fraction 
__________
fraction start, a over b / 2, end of fraction fraction start. a over b slash 2. fraction end. a numerator b / 2 denominator fraction
Torture Test 6: a 0 + 1 a 1 + 1 a 2 + 1 a 3 + 1 a 4 __________
a
sub 

plus 
fraction 

all over 
a
sub 

plus 
fraction 

all over 
a
sub 

plus 
fraction 

all over 
a
sub 

plus 
fraction 

over 
a
sub 

end fraction 
end fraction 
end fraction 
end fraction 
__________
 
a, subscript 0, + fraction start, 1 over a, subscript 1, + fraction start, 1 over a, subscript 2, + fraction start, 1 over a, subscript 3, + fraction start, 1 over a, subscript 4, fraction end, fraction end, fraction end, fraction end a. subscript 0. plus fraction start. 1 over a. subscript 1. plus fraction start. 1 over a. subscript 2. plus fraction start. 1 over a. subscript 3. plus fraction start. 1 over a. subscript 4. fraction end. fraction end. fraction end. fraction end.
 
a base 0 subscript scripted + 1 numerator a base 1 subscript scripted + 1 numerator a base 2 subscript scripted + 1 numerator a base 3 subscript scripted + 1 numerator a base 3 subscript scripted + 1 numerator a base 4 subscript scripted denominator fraction denominator fraction denominator fraction denominator fraction
Torture Test 7: a 0 + 1 a 1 + 1 a 2 + 1 a 3 + 1 a 4 __________
a
sub 

plus 
fraction 

all over 
a
sub 

plus 
fraction 

all over 
a
sub 

plus 
fraction 

all over 
a
sub 

plus 
fraction 

over 
a
sub 

end fraction 
end fraction 
end fraction 
end fraction 
 
__________
a, subscript 0, + fraction start, 1 over a, subscript 1, + fraction start, 1 over a, subscript 2, + fraction start, 1 over a, subscript 3, + fraction start, 1 over a, subscript 4, fraction end, fraction end, fraction end, fraction end a. subscript 0. plus fraction start. 1 over a. subscript 1. plus fraction start. 1 over a. subscript 2. plus fraction start. 1 over a. subscript 3. plus fraction start. 1 over a. subscript 4. fraction end. fraction end. fraction end. fraction end.
 
a base 0 subscript scripted + 1 numerator a base 1 subscript scripted + 1 numerator a base 2 subscript scripted + 1 numerator a base 3 subscript scripted + 1 numerator a base 3 subscript scripted + 1 numerator a base 4 subscript scripted denominator fraction denominator fraction denominator fraction denominator fraction
Torture Test 8: ( n k / 2 ) No output

( fraction start, n over k / 2, end of fraction, )

See WebKit's bug 146454

left paren fraction without bar, start. n over k slash 2. fraction end. right paren ( open-fence n numerator k / 2 denominator fraction without bar ) close-fence
Torture Test 9: ( p 2 ) x 2 y p - 2 - 1 1 - x 1 1 - x 2 No output

( fraction start, p over 2, end of fraction, ), x squared y, superscript p - 2, - fraction start, 1 over 1 - x, end of fraction, fraction start, 1 over 1 - x, squared, end of fraction

See WebKit's bug 146454

left paren fraction without bar, start. p over 2. fraction end. right paren x. superscript 2. y. superscript p minus 2. minus fraction start. 1 over 1 minus x. fraction end. fraction start. 1 over 1 minus x. superscript 2. fraction end.  
Torture Test 10: 0 i m 0 < j < n P ( i , j ) __________
sum 
over 
fraction 

is less than or equal to 

is less than or equal to 

over 

is less than 

is less than 

end fraction 
of 
cap pee of 
open 

comma 

close 
__________

∑ P (i, j)

See WebKit's bug 146407

sum. underscript fraction without bar, start. 0 less than or equal to i less than or equal to m over 0 less than j less than n. fraction end. P left paren i comma j right paren  
Torture Test 11: x 2 y __________
x raised to the 


power 
__________
x, superscript 2 y x. superscript 2 y.  
Torture Test 12: i = 1 p j = 1 q k = 1 r a i j b j k c k i __________
the 
sum 
from 

is equal to 

to 
pee 
of 
the 
sum 
from 

is equal to 

to 

of 
the 
sum 
from 

is equal to 

to 

of 
a
sub 


end sub 
b sub 


end sub 
c sub 


end sub 
__________

∑, with p underneath, ∑, with q underneath, ∑, with r underneath, a, subscript i j, b, subscript j k, c, subscript k i

See WebKit's bug 146407

sum. underscript i equals 1. overscript p. sum. underscript j equals 1. overscript q. sum. underscript k equals 1. overscript r. a. subscript i j. b. subscript j k. c. subscript k i.
 
 
Torture Test 13: 1 + 1 + 1 + 1 + 1 + 1 + 1 + x __________
the square root of the quantity 

plus 
the square root of the quantity 

plus 
the square root of the quantity 

plus 
the square root of the quantity 

plus 
the square root of the quantity 

plus 
the square root of the quantity 

plus 
the square root of the quantity 

plus 

end root 
end root 
end root 
end root 
end root 
end root 
end root 
__________

square root of 1, end of root

See WebKit's bug 146452

square root of 1 plus square root of 1 plus square root of 1 plus square root of 1 plus square root of 1 plus square root of 1 plus square root of 1 plus x. root end. root end. root end. root end. root end. root end. root end.  
Torture Test 14: ( 2 x 2 + 2 y 2 ) | φ ( x + i y ) | 2 = 0 __________
open 
the 
second partialderivative with respect to 

of 
plus 
fraction 
the partial derivative of 
squared 
over 
the partial derivative of 

squared 
end fraction 
close 
times 
the absolute value of 
phi 
open 

plus 


close 
end absolute value 
squared 
is equal to 
0
__________
( fraction start, ∂ squared over ∂ x squared, end of fraction, + fraction start, ∂ squared over ∂ y squared, end of fraction, ), | ϕ ( x + i y ) | squared = 0 left paren fraction start. partial differential. superscript 2. over partial differential x. superscript 2. fraction end. plus fraction start. partial differential. superscript 2. over partial differential y. superscript 2. fraction end. right paren vertical bar φ  left paren x plus i y right paren vertical bar. superscript 2. equals 0  
Torture Test 15: 2 2 2 x __________
2 raised to the 
2 raised to the 

raised to the 

power 
power 
__________
2 to the 2 to the 2, superscript x 2. superscript 2. superscript 2. superscript x.  
Torture Test 16: 1 x dt t __________
the 
integral 
from 

to 

of 
times 
fraction 


over 

end fraction 
__________
integral, subscript 1, superscript x, fraction stary, d t over t, end of fraction integral. subscript 1. superscript x. fraction start. d t over t. fraction end.  
Torture Test 17: D dx dy __________
double integral 
over 
cap d 
of 




__________

∬, subscript D, dxdy

WebKit's bug 146505

double integral. subscript D. d x d y  
Torture Test 18: f ( x ) = { 1 / 3 if  0 x 1 ; 2 / 3 if  3 x 4 ; 0 elsewhere. __________
f of 
 

 
is equal to 
left brace 
table with 3 rows and 2 columns 
row 1 
column 1 

divided by 

column 2 
if  

is less than or equal to 

is less than or equal to 


row 2 
column 1 

divided by 

column 2 
if  

is less than or equal to 

is less than or equal to 


row 3 
column 1 

column 2 
elsewhere. 
end table 
__________
f ( x ) = { Table start, Row 1, Column 1, 1 / 3, Row 1, Column 2, if 0 ≤ x ≤ 1;, Row 2, Column 1, 2 / 3, Row 2, Column 2, if 3 ≤ x ≤ 4;, Row 3, Column 1, 0, Row 3, Column 2, elsewhere., table end

f left paren x right paren equals left brace math table with 3 rows 2 columns. row 1. 1 slash 3. if  0 less than or equal to x less than or equal to 1 semicolon. row 2. 2 slash 3. if  3 less than or equal to x less than or equal to 4 semicolon. row 3. 0. elsewhere. table end.'

 
Torture Test 19: x + ... + x k times __________
modified 

plus 
... 
positive 
x with 
modified 
over brace with 

times 
above 
above 
__________

x + ... + x, with ⏞, with k times underneath underneath

See WebKit's bug 146407

x plus ... plus x. overscript top brace. overscript k times.  
Torture Test 20: y x 2 __________
y sub 

squared 
end sub 
__________
y, subscrit x squared y. subscript x. superscript 2.  
Torture Test 21: p  prime f ( p ) = t > 1 f ( t ) d π ( t ) __________
sum 
over 
pee 
 prime 
of 
f of 
 
pee 
 
is equal to 
integral 
over 

is greater than 

of 
f of 
 

 

pi of 
open 

close 
__________

∑ f ( p ) = ∫, subscript t > 1, f ( t ) d π ( t )

See WebKit's bug 146407

sum. underscript p  prime. f left paren p right paren equals integral. subscript t greater 1. f left paren t right paren d π left paren t right paren
 
 
Torture Test 22: { ( a , ... , a k   a 's , ( b , ... , b   b 's k +  elements } __________
the set 
modified 
modified 
a
comma 
... 
comma 
a
with 
modified 
over brace with 

  
a
apostraphes 
above 
above 
comma 
modified 

comma 
... 
comma 
b with 
modified 
over brace with 
script l 
  

apostraphes 
above 
above with 
modified 
under brace with 

plus 
script l 
 elements 
below 
below 
end set 
__________

{ a , ... , a, with ⏞, with k  a 's underneath, , b , ... , b with ⏞, with ℓ b's underneath underneath, }

See WebKit's bug 146407 and WebKit's bug 146631.

left brace a comma ... comma a. overscript top brace. overscript k  a 's. comma b comma ... comma b. overscript top brace. overscript l  b 's. underscript bottom brace. underscript k plus l elements. right brace

 
Torture Test 23: ( ( a b c d ) ( e f g h ) 0 ( i j k l ) ) __________
matrix with 2 rows and 2 columns 
row 1 
column 1 
matrix with 2 rows and 2 columns 
row 1 
 
a
 

row 2 
 

 

end matrix 
column 2 
matrix with 2 rows and 2 columns 
row 1 
 

 

row 2 
 

 

end matrix 
row 2 
column 1 

column 2 
matrix with 2 rows and 2 columns 
row 1 
 

 

row 2 
 

 

end matrix 
end matrix
__________
( Table start, Row 1, Column 1, ( Table start, Row 1, Column 1, a, Row 1, Column 2, b, Row 2, Column 2, c, Row 2 Column 2, d, table end, ), Row 1, Column 2, ( Table start, Row 1, Column 1, e, Row 1, Column 2, f, Row 2, Column 2, g, Row 2 Column 2, h, table end, ), Row 2, Column 1, 0, Row 2, Column 2, ( Table start, Row 1, Column 1, i, Row 1, Column 2, j, Row 2, Column 2, k, Row 2 Column 2, l, table end, ), table end, ) left paren math table with 2 rows 2 columns. row 1. left paren nested math table with 2 rows 2 columns. row 1. a. b. row 2. c. d. nested table end. right paren. left paren nested math table with 2 rows 2 columns. row 1. e. f. row 2. g. h. nested table end. right paren. row 2. 0. left paren nested math table with 2 rows 2 columns. row 1. i. j. row 2. k. l. nested table end. right paren. table end. right paren  
Torture Test 24: det | c 0 c 1 c 2 c n c 1 c 2 c 3 c n + 1 c 2 c 3 c 4 c n + 2 c n c n + 1 c n + 2 c 2 n | > 0 __________
determinant with 5 rows and 5 columns 
row 1 
column 1 
c sub 

column 2 
c sub 

column 3 
c sub 

column 4 
dot dot dot 
column 5 
c sub 

row 2 
column 1 
c sub 

column 2 
c sub 

column 3 
c sub 

column 4 
dot dot dot 
column 5 
c sub 

plus 

end sub 
row 3 
column 1 
c sub 

column 2 
c sub 

column 3 
c sub 

column 4 
dot dot dot 
column 5 
c sub 

plus 

end sub 
row 4 
column 1 
vertical ellipsis 
column 2 
vertical ellipsis 
column 3 
vertical ellipsis 
column 4 
column 5 
vertical ellipsis 
row 5 
column 1 
c sub 

column 2 
c sub 

plus 

end sub 
column 3 
c sub 

plus 

end sub 
column 4 
dot dot dot 
column 5 
c sub 


end sub 
end determinant 
is greater than 

__________
det | Table Start, Row 1, Column 1, c subscript 0, Row 1, Column 2, c subscript 1, Row 1, Column 3, c subscript 2, Row 1, Column 4, ..., Row 1, Column 5, c subscript n, Row 2, Column 1, c subscript 1, Row 2, Column 2, c subscript 2, Row 2, Column 3, c subscript 3, Row 2, Column 4, ..., Row 2, Column 5, c subscript n + 1, Row 3, Column 1, c subscript 2, Row 3, Column 2, c subscript 3, Row 3, Column 3, c subscript 4, Row 3, Column 4, ..., Row 3, Column 5, c subscript n + 2, Row 4, Column 1, c ⋮, Row 4, Column 2, ⋮, Row 4, Column 3, ⋮, Row 4, Column 4, blank, Row 4, Column 5, ⋮, Row 5, Column 1, c subscript n, Row 5, Column 2, c subscript n + 1, Row 5, Column 3, c subscript n + 2, Row 5, Column 4, ..., Row 5, Column 5, c subscript 2 n, table end, | > 0 det vertical bar math table with 5 rows 5 columns. row 1. c. subscript 0. c. subscript 1. c. subscript 2. horizontal ellipsis. c. subscript n. row 2. c. subscript 1. c. subscript 2. c. subscript 3. horizontal ellipsis. c. subscript n plus 1. row 3. c. subscript 2. c. subscript 3. c. subscript 4. horizontal ellipsis. c. subscript n plus 2. row 4. vertical ellipsis. vertical ellipsis. vertical ellipsis. blank. vertical ellipsis. row 5. c. subscript n. c. subscript n plus 1. c. subscript n plus 2. horizontal ellipsis. c. subscript 2 n. table end. vertical bar greater than 0  
Torture Test 25: y x 2 __________
y sub 
x sub 

end sub 
__________
y, subscript x, subscript 2, y. subscript x. subscript 2.  
Torture Test 26: x 92 31415 + π __________

sub 
92 
to the 
31400 fifteenth  
plus 
pi 
__________
x, subscript 92, to the 31415, + π x. subscript 92. superscript 31415. plus π 
 
 
Torture Test 27: x y b a z c d __________
 

with subscript 

sub 

to the 
a
 
and with superscript 

sub 

to the 
d
 
end sub-superscript 
__________
x, subscript y, subscript b, superscript a, superscript z, subscript c, superscript d x. subscript y. subscript b. superscript a. superscript z. subscript c. superscript d.   
Torture Test 28: y 3 __________

with subscript 

and with superscript 
triple prime 
end sub-superscript
__________
y, subscript 3, superscript ‴ y. subscript 3. superscript triple prime. y base 3 subscript ‴ superscript scripted
d t = φ = 1 + 5 2   , {\displaystyle {\frac {d}{t}}=\varphi ={\frac {1+{\sqrt {5}}}{2}}\ ,}        
d = t × φ   = R   5 + 5 2 = 2 R cos 18 = 2 R cos π 10 1.90211303259 R .        

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