View source for Template:Math/testcases

{{template test cases notice}}

This page is for testing in the Cologne Blue, Modern, Monobook and Vector skins. Sans-serif / serif scaling ratio is 118%.

==Escaping symbols==
:Also, {{button|preview}} warning can be checked 

;basic
*{{test case |1= { ''z'' : ℐ{{sub|''m''}} ''z'' > 0 } and ''u''(''t'') {{=}} ℛ{{sub|''e''}} ''f'' ( ''t'' + 0·''i'' ), then  ℐ{{sub|''m''}} ''f'' ( ''t'' + 0·''i'' ) {{=}} ''H''(''u'')(''t'') |_showcode=y}} {{aye}}
===The <nowiki>=</nowiki>-sign===
* {{test case | 1+2=3 |_showcode=y}} {{nay}}
::<nowiki>{{=}}</nowiki>
*{{test case | 1+2{{=}}3 |_showcode=y}}{{aye}}

=== Using unnamed parameter 1 ===

* {{test case | 1+2=3 |_showcode=y}}{{nay}}

* {{test case |1= 1+2=3 |_showcode=y}}{{aye}}

===The {{!}}-sign (pipe)===
* {{test case |a abs: | a | |_showcode=y}}{{nay}}
::<nowiki>{{!}}</nowiki>
* {{test case |1=a abs: {{!}} a {{!}} |_showcode=y}}{{aye}}

::blank positional
* {{test case |a abs: | a | is a abs | |_showcode=y}}{{nay}}

::using <nowiki>{{!}}</nowiki>
* {{test case |a abs: {{!}} a {{!}} is a abs {{!}} |_showcode=y}}{{aye}}

==Times New Roman (current template)==
:''(font-family: 'Times New Roman', 'Nimbus Roman No9 L', Times, serif;)''

A compact way of rephrasing the point that the base-{{math|''b''}} logarithm of {{math|''y''}} is the solution {{math|''x''}} to the equation {{math|''f''(''x'') {{=}} ''b''<sup>''x''</sup> {{=}} ''y''}} is to say that the logarithm function is the [[inverse function]] of the exponential function. Inverse functions are closely related to the original functions: the [[graph of a function|graphs]] of the two correspond to each other upon reflecting them at the [[diagonal]] line {{math|''x'' {{=}} ''y''}}, as shown at the right: a point {{math|(''t'', ''u'' {{=}} ''b''<sup>''t''</sup>)}} on the graph of the exponential function yields a point {{math|(''u'', ''t'' {{=}} log<sub>''b''</sub>''u'')}} on the graph of the logarithm and vice versa. Moreover, analytic properties of the function pass to its inverse function. Thus, as the exponential function {{math|''f''(''x'') {{=}} ''b''<sup>''x''</sup>}} is [[continuous function|continuous]] and [[differentiable function|differentiable]], so is its inverse function, {{math|log<sub>''b''</sub>(''x'')}}. Roughly speaking, a differentiable function is one whose graph has no sharp "corners".

==Computer Modern Unicode, Times New Roman (/sandbox1)==
:''(font-family: 'CMU Serif', 'Times New Roman', 'Nimbus Roman No9 L', Times, serif;)''

A compact way of rephrasing the point that the base-{{math/sandbox1|''b''}} logarithm of {{math/sandbox1|''y''}} is the solution {{math/sandbox1|''x''}} to the equation {{math/sandbox1|''f''(''x'') {{=}} ''b''<sup>''x''</sup> {{=}} ''y''}} is to say that the logarithm function is the [[inverse function]] of the exponential function. Inverse functions are closely related to the original functions: the [[graph of a function|graphs]] of the two correspond to each other upon reflecting them at the [[diagonal]] line {{math/sandbox1|''x'' {{=}} ''y''}}, as shown at the right: a point {{math/sandbox1|(''t'', ''u'' {{=}} ''b''<sup>''t''</sup>)}} on the graph of the exponential function yields a point {{math/sandbox1|(''u'', ''t'' {{=}} log<sub>''b''</sub>''u'')}} on the graph of the logarithm and vice versa. Moreover, analytic properties of the function pass to its inverse function. Thus, as the exponential function {{math/sandbox1|''f''(''x'') {{=}} ''b''<sup>''x''</sup>}} is [[continuous function|continuous]] and [[differentiable function|differentiable]], so is its inverse function, {{math/sandbox1|log<sub>''b''</sub>(''x'')}}. Roughly speaking, a differentiable function is one whose graph has no sharp "corners".

==Palatino Linotype (/sandbox2)==
:''(font-family: 'Palatino Linotype', 'URW Palladio L', Palatino, serif;)''

A compact way of rephrasing the point that the base-{{math/sandbox2|''b''}} logarithm of {{math/sandbox2|''y''}} is the solution {{math/sandbox2|''x''}} to the equation {{math/sandbox2|''f''(''x'') {{=}} ''b''<sup>''x''</sup> {{=}} ''y''}} is to say that the logarithm function is the [[inverse function]] of the exponential function. Inverse functions are closely related to the original functions: the [[graph of a function|graphs]] of the two correspond to each other upon reflecting them at the [[diagonal]] line {{math/sandbox2|''x'' {{=}} ''y''}}, as shown at the right: a point {{math/sandbox2|(''t'', ''u'' {{=}} ''b''<sup>''t''</sup>)}} on the graph of the exponential function yields a point {{math/sandbox2|(''u'', ''t'' {{=}} log<sub>''b''</sub>''u'')}} on the graph of the logarithm and vice versa. Moreover, analytic properties of the function pass to its inverse function. Thus, as the exponential function {{math/sandbox2|''f''(''x'') {{=}} ''b''<sup>''x''</sup>}} is [[continuous function|continuous]] and [[differentiable function|differentiable]], so is its inverse function, {{math/sandbox2|log<sub>''b''</sub>(''x'')}}. Roughly speaking, a differentiable function is one whose graph has no sharp "corners".

==Century Schoolbook (/sandbox3)==
:''(font-family: 'Century Schoolbook', 'Century Schoolbook L', serif;)''

A compact way of rephrasing the point that the base-{{math/sandbox3|''b''}} logarithm of {{math/sandbox3|''y''}} is the solution {{math/sandbox3|''x''}} to the equation {{math/sandbox3|''f''(''x'') {{=}} ''b''<sup>''x''</sup> {{=}} ''y''}} is to say that the logarithm function is the [[inverse function]] of the exponential function. Inverse functions are closely related to the original functions: the [[graph of a function|graphs]] of the two correspond to each other upon reflecting them at the [[diagonal]] line {{math/sandbox3|''x'' {{=}} ''y''}}, as shown at the right: a point {{math/sandbox3|(''t'', ''u'' {{=}} ''b''<sup>''t''</sup>)}} on the graph of the exponential function yields a point {{math/sandbox3|(''u'', ''t'' {{=}} log<sub>''b''</sub>''u'')}} on the graph of the logarithm and vice versa. Moreover, analytic properties of the function pass to its inverse function. Thus, as the exponential function {{math/sandbox3|''f''(''x'') {{=}} ''b''<sup>''x''</sup>}} is [[continuous function|continuous]] and [[differentiable function|differentiable]], so is its inverse function, {{math/sandbox3|log<sub>''b''</sub>(''x'')}}. Roughly speaking, a differentiable function is one whose graph has no sharp "corners".

==Cambria (/sandbox4)==
:''(font-family: Cambria, serif;)''

A compact way of rephrasing the point that the base-{{math/sandbox4|''b''}} logarithm of {{math/sandbox4|''y''}} is the solution {{math/sandbox4|''x''}} to the equation {{math/sandbox4|''f''(''x'') {{=}} ''b''<sup>''x''</sup> {{=}} ''y''}} is to say that the logarithm function is the [[inverse function]] of the exponential function. Inverse functions are closely related to the original functions: the [[graph of a function|graphs]] of the two correspond to each other upon reflecting them at the [[diagonal]] line {{math/sandbox4|''x'' {{=}} ''y''}}, as shown at the right: a point {{math/sandbox4|(''t'', ''u'' {{=}} ''b''<sup>''t''</sup>)}} on the graph of the exponential function yields a point {{math/sandbox4|(''u'', ''t'' {{=}} log<sub>''b''</sub>''u'')}} on the graph of the logarithm and vice versa. Moreover, analytic properties of the function pass to its inverse function. Thus, as the exponential function {{math/sandbox4|''f''(''x'') {{=}} ''b''<sup>''x''</sup>}} is [[continuous function|continuous]] and [[differentiable function|differentiable]], so is its inverse function, {{math/sandbox4|log<sub>''b''</sub>(''x'')}}. Roughly speaking, a differentiable function is one whose graph has no sharp "corners".

==Constantia (/sandbox5)==
:''(font-family: Constantia, serif)''

A compact way of rephrasing the point that the base-{{math/sandbox5|''b''}} logarithm of {{math/sandbox5|''y''}} is the solution {{math/sandbox5|''x''}} to the equation {{math/sandbox5|''f''(''x'') {{=}} ''b''<sup>''x''</sup> {{=}} ''y''}} is to say that the logarithm function is the [[inverse function]] of the exponential function. Inverse functions are closely related to the original functions: the [[graph of a function|graphs]] of the two correspond to each other upon reflecting them at the [[diagonal]] line {{math/sandbox5|''x'' {{=}} ''y''}}, as shown at the right: a point {{math/sandbox5|(''t'', ''u'' {{=}} ''b''<sup>''t''</sup>)}} on the graph of the exponential function yields a point {{math/sandbox5|(''u'', ''t'' {{=}} log<sub>''b''</sub>''u'')}} on the graph of the logarithm and vice versa. Moreover, analytic properties of the function pass to its inverse function. Thus, as the exponential function {{math/sandbox5|''f''(''x'') {{=}} ''b''<sup>''x''</sup>}} is [[continuous function|continuous]] and [[differentiable function|differentiable]], so is its inverse function, {{math/sandbox5|log<sub>''b''</sub>(''x'')}}. Roughly speaking, a differentiable function is one whose graph has no sharp "corners".

==abs ==
* {{math||''x''||}}