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0001 <!-- this file is autogenerated, if any change has to be done, please fix kdeedu/kalgebra/utils/main.cpp and its dependencies. Thank you, Aleix Pol --><chapter id='commands'>
0002 <title>Commands supported by KAlgebra</title>
0003 <sect1 id='plus'><title>plus</title><itemizedlist>
0004 <listitem><para>Name: plus</para></listitem>
0005 <listitem><para>Description: Addition</para></listitem>
0006 <listitem><para>Parameters: plus(... parameters, ...)</para></listitem>
0007 <listitem><para>Example: x->x+2</para></listitem>
0008 </itemizedlist></sect1>
0009 <sect1 id='times'><title>times</title><itemizedlist>
0010 <listitem><para>Name: times</para></listitem>
0011 <listitem><para>Description: Multiplication</para></listitem>
0012 <listitem><para>Parameters: times(... parameters, ...)</para></listitem>
0013 <listitem><para>Example: x->x*2</para></listitem>
0014 </itemizedlist></sect1>
0015 <sect1 id='minus'><title>minus</title><itemizedlist>
0016 <listitem><para>Name: minus</para></listitem>
0017 <listitem><para>Description: Subtraction. Will remove all values from the first one.</para></listitem>
0018 <listitem><para>Parameters: minus(... parameters, ...)</para></listitem>
0019 <listitem><para>Example: x->x-2</para></listitem>
0020 </itemizedlist></sect1>
0021 <sect1 id='divide'><title>divide</title><itemizedlist>
0022 <listitem><para>Name: divide</para></listitem>
0023 <listitem><para>Description: Division</para></listitem>
0024 <listitem><para>Parameters: divide(par1, par2)</para></listitem>
0025 <listitem><para>Example: x->x/2</para></listitem>
0026 </itemizedlist></sect1>
0027 <sect1 id='quotient'><title>quotient</title><itemizedlist>
0028 <listitem><para>Name: quotient</para></listitem>
0029 <listitem><para>Description: Quotient</para></listitem>
0030 <listitem><para>Parameters: quotient(par1, par2)</para></listitem>
0031 <listitem><para>Example: x->quotient(x, 2)</para></listitem>
0032 </itemizedlist></sect1>
0033 <sect1 id='power'><title>power</title><itemizedlist>
0034 <listitem><para>Name: power</para></listitem>
0035 <listitem><para>Description: Power</para></listitem>
0036 <listitem><para>Parameters: power(par1, par2)</para></listitem>
0037 <listitem><para>Example: x->x^2</para></listitem>
0038 </itemizedlist></sect1>
0039 <sect1 id='root'><title>root</title><itemizedlist>
0040 <listitem><para>Name: root</para></listitem>
0041 <listitem><para>Description: Root</para></listitem>
0042 <listitem><para>Parameters: root(par1, par2)</para></listitem>
0043 <listitem><para>Example: x->root(x, 2)</para></listitem>
0044 </itemizedlist></sect1>
0045 <sect1 id='factorial'><title>factorial</title><itemizedlist>
0046 <listitem><para>Name: factorial</para></listitem>
0047 <listitem><para>Description: Factorial. factorial(n)=n!</para></listitem>
0048 <listitem><para>Parameters: factorial(par1)</para></listitem>
0049 <listitem><para>Example: x->factorial(x)</para></listitem>
0050 </itemizedlist></sect1>
0051 <sect1 id='and'><title>and</title><itemizedlist>
0052 <listitem><para>Name: and</para></listitem>
0053 <listitem><para>Description: Boolean and</para></listitem>
0054 <listitem><para>Parameters: and(... parameters, ...)</para></listitem>
0055 <listitem><para>Example: x->piecewise { and(x>-2, x<2) ? 1, ? 0 }</para></listitem>
0056 </itemizedlist></sect1>
0057 <sect1 id='or'><title>or</title><itemizedlist>
0058 <listitem><para>Name: or</para></listitem>
0059 <listitem><para>Description: Boolean or</para></listitem>
0060 <listitem><para>Parameters: or(... parameters, ...)</para></listitem>
0061 <listitem><para>Example: x->piecewise { or(x>2, x>-2) ? 1, ? 0 }</para></listitem>
0062 </itemizedlist></sect1>
0063 <sect1 id='xor'><title>xor</title><itemizedlist>
0064 <listitem><para>Name: xor</para></listitem>
0065 <listitem><para>Description: Boolean xor</para></listitem>
0066 <listitem><para>Parameters: xor(... parameters, ...)</para></listitem>
0067 <listitem><para>Example: x->piecewise { xor(x>0, x<3) ? 1, ? 0 }</para></listitem>
0068 </itemizedlist></sect1>
0069 <sect1 id='not'><title>not</title><itemizedlist>
0070 <listitem><para>Name: not</para></listitem>
0071 <listitem><para>Description: Boolean not</para></listitem>
0072 <listitem><para>Parameters: not(par1)</para></listitem>
0073 <listitem><para>Example: x->piecewise { not(x>0) ? 1, ? 0 }</para></listitem>
0074 </itemizedlist></sect1>
0075 <sect1 id='gcd'><title>gcd</title><itemizedlist>
0076 <listitem><para>Name: gcd</para></listitem>
0077 <listitem><para>Description: Greatest common divisor</para></listitem>
0078 <listitem><para>Parameters: gcd(... parameters, ...)</para></listitem>
0079 <listitem><para>Example: x->gcd(x, 3)</para></listitem>
0080 </itemizedlist></sect1>
0081 <sect1 id='lcm'><title>lcm</title><itemizedlist>
0082 <listitem><para>Name: lcm</para></listitem>
0083 <listitem><para>Description: Least common multiple</para></listitem>
0084 <listitem><para>Parameters: lcm(... parameters, ...)</para></listitem>
0085 <listitem><para>Example: x->lcm(x, 4)</para></listitem>
0086 </itemizedlist></sect1>
0087 <sect1 id='rem'><title>rem</title><itemizedlist>
0088 <listitem><para>Name: rem</para></listitem>
0089 <listitem><para>Description: Remainder</para></listitem>
0090 <listitem><para>Parameters: rem(par1, par2)</para></listitem>
0091 <listitem><para>Example: x->rem(x, 5)</para></listitem>
0092 </itemizedlist></sect1>
0093 <sect1 id='factorof'><title>factorof</title><itemizedlist>
0094 <listitem><para>Name: factorof</para></listitem>
0095 <listitem><para>Description: The factor of</para></listitem>
0096 <listitem><para>Parameters: factorof(par1, par2)</para></listitem>
0097 <listitem><para>Example: x->factorof(x, 3)</para></listitem>
0098 </itemizedlist></sect1>
0099 <sect1 id='max'><title>max</title><itemizedlist>
0100 <listitem><para>Name: max</para></listitem>
0101 <listitem><para>Description: Maximum</para></listitem>
0102 <listitem><para>Parameters: max(... parameters, ...)</para></listitem>
0103 <listitem><para>Example: x->max(x, 4)</para></listitem>
0104 </itemizedlist></sect1>
0105 <sect1 id='min'><title>min</title><itemizedlist>
0106 <listitem><para>Name: min</para></listitem>
0107 <listitem><para>Description: Minimum</para></listitem>
0108 <listitem><para>Parameters: min(... parameters, ...)</para></listitem>
0109 <listitem><para>Example: x->min(x, 4)</para></listitem>
0110 </itemizedlist></sect1>
0111 <sect1 id='lt'><title>lt</title><itemizedlist>
0112 <listitem><para>Name: lt</para></listitem>
0113 <listitem><para>Description: Less than. lt(a,b)=a<b</para></listitem>
0114 <listitem><para>Parameters: lt(par1, par2)</para></listitem>
0115 <listitem><para>Example: x->piecewise { x<4 ? 1, ? 0 }</para></listitem>
0116 </itemizedlist></sect1>
0117 <sect1 id='gt'><title>gt</title><itemizedlist>
0118 <listitem><para>Name: gt</para></listitem>
0119 <listitem><para>Description: Greater than. gt(a,b)=a>b</para></listitem>
0120 <listitem><para>Parameters: gt(par1, par2)</para></listitem>
0121 <listitem><para>Example: x->piecewise { x>4 ? 1, ? 0 }</para></listitem>
0122 </itemizedlist></sect1>
0123 <sect1 id='eq'><title>eq</title><itemizedlist>
0124 <listitem><para>Name: eq</para></listitem>
0125 <listitem><para>Description: Equal. eq(a,b) = a=b</para></listitem>
0126 <listitem><para>Parameters: eq(par1, par2)</para></listitem>
0127 <listitem><para>Example: x->piecewise { x=4 ? 1, ? 0 }</para></listitem>
0128 </itemizedlist></sect1>
0129 <sect1 id='neq'><title>neq</title><itemizedlist>
0130 <listitem><para>Name: neq</para></listitem>
0131 <listitem><para>Description: Not equal. neq(a,b)=a≠b</para></listitem>
0132 <listitem><para>Parameters: neq(par1, par2)</para></listitem>
0133 <listitem><para>Example: x->piecewise { x!=4 ? 1, ? 0 }</para></listitem>
0134 </itemizedlist></sect1>
0135 <sect1 id='leq'><title>leq</title><itemizedlist>
0136 <listitem><para>Name: leq</para></listitem>
0137 <listitem><para>Description: Less or equal. leq(a,b)=a≤b</para></listitem>
0138 <listitem><para>Parameters: leq(par1, par2)</para></listitem>
0139 <listitem><para>Example: x->piecewise { x<=4 ? 1, ? 0 }</para></listitem>
0140 </itemizedlist></sect1>
0141 <sect1 id='geq'><title>geq</title><itemizedlist>
0142 <listitem><para>Name: geq</para></listitem>
0143 <listitem><para>Description: Greater or equal. geq(a,b)=a≥b</para></listitem>
0144 <listitem><para>Parameters: geq(par1, par2)</para></listitem>
0145 <listitem><para>Example: x->piecewise { x>=4 ? 1, ? 0 }</para></listitem>
0146 </itemizedlist></sect1>
0147 <sect1 id='implies'><title>implies</title><itemizedlist>
0148 <listitem><para>Name: implies</para></listitem>
0149 <listitem><para>Description: Boolean implication</para></listitem>
0150 <listitem><para>Parameters: implies(par1, par2)</para></listitem>
0151 <listitem><para>Example: x->piecewise { implies(x<0, x<3) ? 1, ? 0 }</para></listitem>
0152 </itemizedlist></sect1>
0153 <sect1 id='approx'><title>approx</title><itemizedlist>
0154 <listitem><para>Name: approx</para></listitem>
0155 <listitem><para>Description: Approximation. approx(a)=a±n</para></listitem>
0156 <listitem><para>Parameters: approx(par1, par2)</para></listitem>
0157 <listitem><para>Example: x->piecewise { approx(x, 4) ? 1, ? 0 }</para></listitem>
0158 </itemizedlist></sect1>
0159 <sect1 id='abs'><title>abs</title><itemizedlist>
0160 <listitem><para>Name: abs</para></listitem>
0161 <listitem><para>Description: Absolute value. abs(n)=|n|</para></listitem>
0162 <listitem><para>Parameters: abs(par1)</para></listitem>
0163 <listitem><para>Example: x->abs(x)</para></listitem>
0164 </itemizedlist></sect1>
0165 <sect1 id='floor'><title>floor</title><itemizedlist>
0166 <listitem><para>Name: floor</para></listitem>
0167 <listitem><para>Description: Floor value. floor(n)=⌊n⌋</para></listitem>
0168 <listitem><para>Parameters: floor(par1)</para></listitem>
0169 <listitem><para>Example: x->floor(x)</para></listitem>
0170 </itemizedlist></sect1>
0171 <sect1 id='ceiling'><title>ceiling</title><itemizedlist>
0172 <listitem><para>Name: ceiling</para></listitem>
0173 <listitem><para>Description: Ceil value. ceil(n)=⌈n⌉</para></listitem>
0174 <listitem><para>Parameters: ceiling(par1)</para></listitem>
0175 <listitem><para>Example: x->ceiling(x)</para></listitem>
0176 </itemizedlist></sect1>
0177 <sect1 id='sin'><title>sin</title><itemizedlist>
0178 <listitem><para>Name: sin</para></listitem>
0179 <listitem><para>Description: Function to calculate the sine of a given angle</para></listitem>
0180 <listitem><para>Parameters: sin(par1)</para></listitem>
0181 <listitem><para>Example: x->sin(x)</para></listitem>
0182 </itemizedlist></sect1>
0183 <sect1 id='cos'><title>cos</title><itemizedlist>
0184 <listitem><para>Name: cos</para></listitem>
0185 <listitem><para>Description: Function to calculate the cosine of a given angle</para></listitem>
0186 <listitem><para>Parameters: cos(par1)</para></listitem>
0187 <listitem><para>Example: x->cos(x)</para></listitem>
0188 </itemizedlist></sect1>
0189 <sect1 id='tan'><title>tan</title><itemizedlist>
0190 <listitem><para>Name: tan</para></listitem>
0191 <listitem><para>Description: Function to calculate the tangent of a given angle</para></listitem>
0192 <listitem><para>Parameters: tan(par1)</para></listitem>
0193 <listitem><para>Example: x->tan(x)</para></listitem>
0194 </itemizedlist></sect1>
0195 <sect1 id='sec'><title>sec</title><itemizedlist>
0196 <listitem><para>Name: sec</para></listitem>
0197 <listitem><para>Description: Secant</para></listitem>
0198 <listitem><para>Parameters: sec(par1)</para></listitem>
0199 <listitem><para>Example: x->sec(x)</para></listitem>
0200 </itemizedlist></sect1>
0201 <sect1 id='csc'><title>csc</title><itemizedlist>
0202 <listitem><para>Name: csc</para></listitem>
0203 <listitem><para>Description: Cosecant</para></listitem>
0204 <listitem><para>Parameters: csc(par1)</para></listitem>
0205 <listitem><para>Example: x->csc(x)</para></listitem>
0206 </itemizedlist></sect1>
0207 <sect1 id='cot'><title>cot</title><itemizedlist>
0208 <listitem><para>Name: cot</para></listitem>
0209 <listitem><para>Description: Cotangent</para></listitem>
0210 <listitem><para>Parameters: cot(par1)</para></listitem>
0211 <listitem><para>Example: x->cot(x)</para></listitem>
0212 </itemizedlist></sect1>
0213 <sect1 id='sinh'><title>sinh</title><itemizedlist>
0214 <listitem><para>Name: sinh</para></listitem>
0215 <listitem><para>Description: Hyperbolic sine</para></listitem>
0216 <listitem><para>Parameters: sinh(par1)</para></listitem>
0217 <listitem><para>Example: x->sinh(x)</para></listitem>
0218 </itemizedlist></sect1>
0219 <sect1 id='cosh'><title>cosh</title><itemizedlist>
0220 <listitem><para>Name: cosh</para></listitem>
0221 <listitem><para>Description: Hyperbolic cosine</para></listitem>
0222 <listitem><para>Parameters: cosh(par1)</para></listitem>
0223 <listitem><para>Example: x->cosh(x)</para></listitem>
0224 </itemizedlist></sect1>
0225 <sect1 id='tanh'><title>tanh</title><itemizedlist>
0226 <listitem><para>Name: tanh</para></listitem>
0227 <listitem><para>Description: Hyperbolic tangent</para></listitem>
0228 <listitem><para>Parameters: tanh(par1)</para></listitem>
0229 <listitem><para>Example: x->tanh(x)</para></listitem>
0230 </itemizedlist></sect1>
0231 <sect1 id='sech'><title>sech</title><itemizedlist>
0232 <listitem><para>Name: sech</para></listitem>
0233 <listitem><para>Description: Hyperbolic secant</para></listitem>
0234 <listitem><para>Parameters: sech(par1)</para></listitem>
0235 <listitem><para>Example: x->sech(x)</para></listitem>
0236 </itemizedlist></sect1>
0237 <sect1 id='csch'><title>csch</title><itemizedlist>
0238 <listitem><para>Name: csch</para></listitem>
0239 <listitem><para>Description: Hyperbolic cosecant</para></listitem>
0240 <listitem><para>Parameters: csch(par1)</para></listitem>
0241 <listitem><para>Example: x->csch(x)</para></listitem>
0242 </itemizedlist></sect1>
0243 <sect1 id='coth'><title>coth</title><itemizedlist>
0244 <listitem><para>Name: coth</para></listitem>
0245 <listitem><para>Description: Hyperbolic cotangent</para></listitem>
0246 <listitem><para>Parameters: coth(par1)</para></listitem>
0247 <listitem><para>Example: x->coth(x)</para></listitem>
0248 </itemizedlist></sect1>
0249 <sect1 id='arcsin'><title>arcsin</title><itemizedlist>
0250 <listitem><para>Name: arcsin</para></listitem>
0251 <listitem><para>Description: Arc sine</para></listitem>
0252 <listitem><para>Parameters: arcsin(par1)</para></listitem>
0253 <listitem><para>Example: x->arcsin(x)</para></listitem>
0254 </itemizedlist></sect1>
0255 <sect1 id='arccos'><title>arccos</title><itemizedlist>
0256 <listitem><para>Name: arccos</para></listitem>
0257 <listitem><para>Description: Arc cosine</para></listitem>
0258 <listitem><para>Parameters: arccos(par1)</para></listitem>
0259 <listitem><para>Example: x->arccos(x)</para></listitem>
0260 </itemizedlist></sect1>
0261 <sect1 id='arctan'><title>arctan</title><itemizedlist>
0262 <listitem><para>Name: arctan</para></listitem>
0263 <listitem><para>Description: Arc tangent</para></listitem>
0264 <listitem><para>Parameters: arctan(par1)</para></listitem>
0265 <listitem><para>Example: x->arctan(x)</para></listitem>
0266 </itemizedlist></sect1>
0267 <sect1 id='arccot'><title>arccot</title><itemizedlist>
0268 <listitem><para>Name: arccot</para></listitem>
0269 <listitem><para>Description: Arc cotangent</para></listitem>
0270 <listitem><para>Parameters: arccot(par1)</para></listitem>
0271 <listitem><para>Example: x->arccot(x)</para></listitem>
0272 </itemizedlist></sect1>
0273 <sect1 id='arccosh'><title>arccosh</title><itemizedlist>
0274 <listitem><para>Name: arccosh</para></listitem>
0275 <listitem><para>Description: Hyperbolic arc cosine</para></listitem>
0276 <listitem><para>Parameters: arccosh(par1)</para></listitem>
0277 <listitem><para>Example: x->arccosh(x)</para></listitem>
0278 </itemizedlist></sect1>
0279 <sect1 id='arccsc'><title>arccsc</title><itemizedlist>
0280 <listitem><para>Name: arccsc</para></listitem>
0281 <listitem><para>Description: Arc cosecant</para></listitem>
0282 <listitem><para>Parameters: arccsc(par1)</para></listitem>
0283 <listitem><para>Example: x->arccsc(x)</para></listitem>
0284 </itemizedlist></sect1>
0285 <sect1 id='arccsch'><title>arccsch</title><itemizedlist>
0286 <listitem><para>Name: arccsch</para></listitem>
0287 <listitem><para>Description: Hyperbolic arc cosecant</para></listitem>
0288 <listitem><para>Parameters: arccsch(par1)</para></listitem>
0289 <listitem><para>Example: x->arccsch(x)</para></listitem>
0290 </itemizedlist></sect1>
0291 <sect1 id='arcsec'><title>arcsec</title><itemizedlist>
0292 <listitem><para>Name: arcsec</para></listitem>
0293 <listitem><para>Description: Arc secant</para></listitem>
0294 <listitem><para>Parameters: arcsec(par1)</para></listitem>
0295 <listitem><para>Example: x->arcsec(x)</para></listitem>
0296 </itemizedlist></sect1>
0297 <sect1 id='arcsech'><title>arcsech</title><itemizedlist>
0298 <listitem><para>Name: arcsech</para></listitem>
0299 <listitem><para>Description: Hyperbolic arc secant</para></listitem>
0300 <listitem><para>Parameters: arcsech(par1)</para></listitem>
0301 <listitem><para>Example: x->arcsech(x)</para></listitem>
0302 </itemizedlist></sect1>
0303 <sect1 id='arcsinh'><title>arcsinh</title><itemizedlist>
0304 <listitem><para>Name: arcsinh</para></listitem>
0305 <listitem><para>Description: Hyperbolic arc sine</para></listitem>
0306 <listitem><para>Parameters: arcsinh(par1)</para></listitem>
0307 <listitem><para>Example: x->arcsinh(x)</para></listitem>
0308 </itemizedlist></sect1>
0309 <sect1 id='arctanh'><title>arctanh</title><itemizedlist>
0310 <listitem><para>Name: arctanh</para></listitem>
0311 <listitem><para>Description: Hyperbolic arc tangent</para></listitem>
0312 <listitem><para>Parameters: arctanh(par1)</para></listitem>
0313 <listitem><para>Example: x->arctanh(x)</para></listitem>
0314 </itemizedlist></sect1>
0315 <sect1 id='exp'><title>exp</title><itemizedlist>
0316 <listitem><para>Name: exp</para></listitem>
0317 <listitem><para>Description: Exponent (e^x)</para></listitem>
0318 <listitem><para>Parameters: exp(par1)</para></listitem>
0319 <listitem><para>Example: x->exp(x)</para></listitem>
0320 </itemizedlist></sect1>
0321 <sect1 id='ln'><title>ln</title><itemizedlist>
0322 <listitem><para>Name: ln</para></listitem>
0323 <listitem><para>Description: Base-e logarithm</para></listitem>
0324 <listitem><para>Parameters: ln(par1)</para></listitem>
0325 <listitem><para>Example: x->ln(x)</para></listitem>
0326 </itemizedlist></sect1>
0327 <sect1 id='log'><title>log</title><itemizedlist>
0328 <listitem><para>Name: log</para></listitem>
0329 <listitem><para>Description: Base-10 logarithm</para></listitem>
0330 <listitem><para>Parameters: log(par1)</para></listitem>
0331 <listitem><para>Example: x->log(x)</para></listitem>
0332 </itemizedlist></sect1>
0333 <sect1 id='conjugate'><title>conjugate</title><itemizedlist>
0334 <listitem><para>Name: conjugate</para></listitem>
0335 <listitem><para>Description: Conjugate</para></listitem>
0336 <listitem><para>Parameters: conjugate(par1)</para></listitem>
0337 <listitem><para>Example: x->conjugate(x*i)</para></listitem>
0338 </itemizedlist></sect1>
0339 <sect1 id='arg'><title>arg</title><itemizedlist>
0340 <listitem><para>Name: arg</para></listitem>
0341 <listitem><para>Description: Arg</para></listitem>
0342 <listitem><para>Parameters: arg(par1)</para></listitem>
0343 <listitem><para>Example: x->arg(x*i)</para></listitem>
0344 </itemizedlist></sect1>
0345 <sect1 id='real'><title>real</title><itemizedlist>
0346 <listitem><para>Name: real</para></listitem>
0347 <listitem><para>Description: Real</para></listitem>
0348 <listitem><para>Parameters: real(par1)</para></listitem>
0349 <listitem><para>Example: x->real(x*i)</para></listitem>
0350 </itemizedlist></sect1>
0351 <sect1 id='imaginary'><title>imaginary</title><itemizedlist>
0352 <listitem><para>Name: imaginary</para></listitem>
0353 <listitem><para>Description: Imaginary</para></listitem>
0354 <listitem><para>Parameters: imaginary(par1)</para></listitem>
0355 <listitem><para>Example: x->imaginary(x*i)</para></listitem>
0356 </itemizedlist></sect1>
0357 <sect1 id='sum'><title>sum</title><itemizedlist>
0358 <listitem><para>Name: sum</para></listitem>
0359 <listitem><para>Description: Summatory</para></listitem>
0360 <listitem><para>Parameters: sum(par1 : var=from..to)</para></listitem>
0361 <listitem><para>Example: x->x*sum(t*t:t=0..3)</para></listitem>
0362 </itemizedlist></sect1>
0363 <sect1 id='product'><title>product</title><itemizedlist>
0364 <listitem><para>Name: product</para></listitem>
0365 <listitem><para>Description: Productory</para></listitem>
0366 <listitem><para>Parameters: product(par1 : var=from..to)</para></listitem>
0367 <listitem><para>Example: x->product(t+t:t=1..3)</para></listitem>
0368 </itemizedlist></sect1>
0369 <sect1 id='diff'><title>diff</title><itemizedlist>
0370 <listitem><para>Name: diff</para></listitem>
0371 <listitem><para>Description: Differentiation</para></listitem>
0372 <listitem><para>Parameters: diff(par1 : var)</para></listitem>
0373 <listitem><para>Example: x->(diff(x^2:x))(x)</para></listitem>
0374 </itemizedlist></sect1>
0375 <sect1 id='card'><title>card</title><itemizedlist>
0376 <listitem><para>Name: card</para></listitem>
0377 <listitem><para>Description: Cardinal</para></listitem>
0378 <listitem><para>Parameters: card(par1)</para></listitem>
0379 <listitem><para>Example: x->card(vector { x, 1, 2 })</para></listitem>
0380 </itemizedlist></sect1>
0381 <sect1 id='scalarproduct'><title>scalarproduct</title><itemizedlist>
0382 <listitem><para>Name: scalarproduct</para></listitem>
0383 <listitem><para>Description: Scalar product</para></listitem>
0384 <listitem><para>Parameters: scalarproduct(... parameters, ...)</para></listitem>
0385 <listitem><para>Example: x->scalarproduct(vector { 0, x }, vector { x, 0 })[1]</para></listitem>
0386 </itemizedlist></sect1>
0387 <sect1 id='selector'><title>selector</title><itemizedlist>
0388 <listitem><para>Name: selector</para></listitem>
0389 <listitem><para>Description: Select the par1-th element of par2 list or vector</para></listitem>
0390 <listitem><para>Parameters: selector(par1, par2)</para></listitem>
0391 <listitem><para>Example: x->scalarproduct(vector { 0, x }, vector { x, 0 })[1]</para></listitem>
0392 </itemizedlist></sect1>
0393 <sect1 id='union'><title>union</title><itemizedlist>
0394 <listitem><para>Name: union</para></listitem>
0395 <listitem><para>Description: Joins several items of the same type</para></listitem>
0396 <listitem><para>Parameters: union(... parameters, ...)</para></listitem>
0397 <listitem><para>Example: x->union(list { 1, 2, 3 }, list { 4, 5, 6 })[rem(floor(x), 5)+3]</para></listitem>
0398 </itemizedlist></sect1>
0399 <sect1 id='forall'><title>forall</title><itemizedlist>
0400 <listitem><para>Name: forall</para></listitem>
0401 <listitem><para>Description: For all</para></listitem>
0402 <listitem><para>Parameters: forall(par1 : var)</para></listitem>
0403 <listitem><para>Example: x->piecewise { forall(t:t@list { true, false, false }) ? 1, ? 0 }</para></listitem>
0404 </itemizedlist></sect1>
0405 <sect1 id='exists'><title>exists</title><itemizedlist>
0406 <listitem><para>Name: exists</para></listitem>
0407 <listitem><para>Description: Exists</para></listitem>
0408 <listitem><para>Parameters: exists(par1 : var)</para></listitem>
0409 <listitem><para>Example: x->piecewise { exists(t:t@list { true, false, false }) ? 1, ? 0 }</para></listitem>
0410 </itemizedlist></sect1>
0411 <sect1 id='map'><title>map</title><itemizedlist>
0412 <listitem><para>Name: map</para></listitem>
0413 <listitem><para>Description: Applies a function to every element in a list</para></listitem>
0414 <listitem><para>Parameters: map(par1, par2)</para></listitem>
0415 <listitem><para>Example: x->map(x->x+x, list { 1, 2, 3, 4, 5, 6 })[rem(floor(x), 5)+3]</para></listitem>
0416 </itemizedlist></sect1>
0417 <sect1 id='filter'><title>filter</title><itemizedlist>
0418 <listitem><para>Name: filter</para></listitem>
0419 <listitem><para>Description: Removes all elements that don't fit a condition</para></listitem>
0420 <listitem><para>Parameters: filter(par1, par2)</para></listitem>
0421 <listitem><para>Example: x->filter(u->rem(u, 2)=0, list { 2, 4, 3, 4, 8, 6 })[rem(floor(x), 5)+3]</para></listitem>
0422 </itemizedlist></sect1>
0423 <sect1 id='transpose'><title>transpose</title><itemizedlist>
0424 <listitem><para>Name: transpose</para></listitem>
0425 <listitem><para>Description: Transpose</para></listitem>
0426 <listitem><para>Parameters: transpose(par1)</para></listitem>
0427 <listitem><para>Example: x->transpose(matrix { matrixrow { 1, 2, 3, 4, 5, 6 } })[rem(floor(x), 5)+3][1]</para></listitem>
0428 </itemizedlist></sect1>
0429 </chapter>