f:=(x)->(exp(x)-x)/(exp(x)+x); #my function

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYsJi1JJGV4cEdGJTYjOSQiIiJGMSEiIkYyLCZGLkYyRjFGMkYzRiVGJUYl

start:=-9.54; # start point

NiM+SSZzdGFydEc2IiQhJGEqISIj

ends:=-1.0; # end point

NiM+SSVlbmRzRzYiJCEjNSEiIg==

sum_:=f(start)+f(ends);

NiM+SSVzdW1fRzYiJCErIlxvUjskISIq

multi:=f(start)*f(ends);

NiM+SSZtdWx0aUc2IiQiK1NnKVI7IyEiKg==

razn:=f(ends)-f(start);

NiM+SSVyYXpuRzYiJCErUCRRUjsiISIq

division:=f(ends)/f(start);

NiM+SSlkaXZpc2lvbkc2IiQiKyp5P1I7IyEiKg==

sin(division); ### 2.2

NiMkIitxSCk+SCkhIzU=

arctan(division);

NiMkIitXZSF6OCIhIio=

ln(division);

NiMkIitqdkA+eCEjNQ==

sqrt(division);

NiMkIis/ci1yOSEiKg==

signum(division);

NiMiIiI=

compl:=ends+start*I; ### 2.3

NiM+SSZjb21wbEc2Il4kJCEjNSEiIiQhJGEqISIj

Re(compl);

NiMkISM1ISIi

Im(compl);

NiMkISRhKiEiIw==

ads(compl);

NiMtSSRhZHNHNiI2I14kJCEjNSEiIiQhJGEqISIj

#restart;f:=(x)->(exp(x)-x)/(exp(x)+x); ### 2.4

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYsJi1JJGV4cEc2JEkqcHJvdGVjdGVkR0YxSShfc3lzbGliR0YlNiM5JCIiIkY0ISIiRjUsJkYuRjVGNEY1RjZGJUYlRiU=

solve(f(x)=0,x);

NiMsJC1JKUxhbWJlcnRXRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2IyEiIkYr

step:=(ends-start)/4;

NiM+SSVzdGVwRzYiJCIrKysrTkAhIio=

X:=array(1..5):Y:=array(1..5): for i to 5 do X[i]:=start+i*step:Y[i]:=f(X[i]) end do: print(X,Y);

NiQtSSd2ZWN0b3JHNiI2IzcnJCErKysrMHUhIiokISsrKytxX0YqJCErKysrTkpGKiQhKysrKys1RiokIiorK104IiEiKS1GJDYjNyckISsjR2ssKyJGKiQhK1VSJj4rIkYqJCErPDo5RzVGKiQhKzlNJlI7I0YqJCIrMS4sYVkhIzU=

func2:=(z)->interp(X,Y,z);

NiM+SSZmdW5jMkc2ImYqNiNJInpHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JJ2ludGVycEc2JEkqcHJvdGVjdGVkR0YvSShfc3lzbGliR0YlNiVJIlhHRiVJIllHRiU5JEYlRiVGJQ==

plot(f(x),x=start..ends);

LSUlUExPVEc2Ji0lJ0NVUlZFU0c2JDdnbjckJCEzOioqKioqKioqKioqKlImKiEjPCQhMzJCNC14XSwrNUYsNyQkITMlZW07TUlfUU4qRiwkITNiXVxDQiY9KysiRiw3JCQhM0tMZSV6PScpPT4qRiwkITMoZVNEUTtBKysiRiw3JCQhM1ptO2ZeJFEoNCEqRiwkITMuNzxrSHItKzVGLDckJCEzWWw7OUBKUUUpKUYsJCEzOGBfTG1LLis1Riw3JCQhM0FLZTRZJCoqUWspRiwkITNrZD83cDIvKzVGLDckJCEzZ2wienFfOFpaKUYsJCEzKSo9OWxbI1wrKyJGLDckJCEzcSlcNzZUSiYqSClGLCQhM0IreCJvIipmKysiRiw3JCQhM19tInpoInlOPSIpRiwkITNtY3UhNFV0KysiRiw3JCQhMzUqXGlzQ2x4JHpGLCQhM3NBSGxhKiozKzVGLDckJCEzI0dMJFsjZi4/dihGLCQhMzAlKXpNOTQ2KzVGLDckJCEzMW07JWVpJVEpZShGLCQhM3pEJ0cjXE04KzVGLDckJCEzJykqKipcQ1UpPS91RiwkITMqXDI1TVZrLCsiRiw3JCQhM1oqKipcPCplQj5zRiwkITMyZlVPN0g/KzVGLDckJCEzQyoqKlx2JikqKjQvKEYsJCEzcSd6XWtrWy0rIkYsNyQkITNHbSJ6SllXInpvRiwkITM9dGEmb0AqSCs1Riw3JCQhMylITCRHV0ZvJ28nRiwkITNzO3FkdEpQKzVGLDckJCEzVUxMOEJDa0JsRiwkITMxVkIwXy1YKzVGLDckJCEzZipcNy14KClSTCdGLCQhMyNwV11xZ2cwKyJGLDckJCEzM0xMam03Nm1oRiwkITNdcG1kdTZvKzVGLDckJCEzNStEQE5UIz4pZkYsJCEzM0x3PT9VJTMrIkYsNyQkITMpKSpcUCdIV2AxZUYsJCEzZGlEYGFsLiw1Riw3JCQhM2hLJGU5bkxOaSZGLCQhMzsxSm92YEcsNUYsNyQkITNhS2V6Wz1bYmFGLCQhMzY/dGlld2MsNUYsNyQkITN5bTsvYl9AdV9GLCQhM2YybCd5Olc+KyJGLDckJCEza20ieiIzLSRmMyZGLCQhMz8pR2phVU1DKyJGLDckJCEzQCt2UUB2LUFcRiwkITN5LUd3JEdrSCsiRiw3JCQhM2htO1JIIjNddSVGLCQhM3hUOWRHO24uNUYsNyQkITMjKioqKio0dyhIQGMlRiwkITMjcCZSaj5zZS81Riw3JCQhM2UrXSNlKSo9S1ElRiwkITMkPT8wcy84ZCsiRiw3JCQhM2sqXDdvZjgsQCVGLCQhM25VJikpeSdvMjI1Riw3JCQhM2ErXShmZDR6LCVGLCQhMz4wTSIpW2EqKjM1Riw3JCQhMyNRTExZcjBfJVFGLCQhM15yckZyTj02NUYsNyQkITMpKSoqKlwoenUhM20kRiwkITMnUT0sNFJZVCwiRiw3JCQhMzVuIno+RjpQXCRGLCQhM2AtXyFbSVt2LCJGLDckJCEzOyoqKlxTTlI1SiRGLCQhMz0pKnBtdCh6QS0iRiw3JCQhM1tNZWFeYjpSSkYsJCEzN3VDa2xiKXotIkYsNyQkITNpKlxpPVgoW2ZIRiwkITMvPlszSzptTjVGLDckJCEzP01MM1chSFF5I0YsJCEzWUFUJ2ZPM2EvIkYsNyQkITM/K0RKcTQkKipmI0YsJCEzSTVQIVFVPillNUYsNyQkITNpbW1Zb18iR1UjRiwkITM1JCozS3F5KGYyIkYsNyQkITM7bjslPikpKW9UQUYsJCEzSyopNClcYFImKjQiRiw3JCQhMyFIJGVNOEIxaT9GLCQhM3UhW1spUkZaSjZGLDckJCEzMSsrNV9UKygqPUYsJCEzMUlLJWY5Vzw8IkYsNyQkITNFTCQzRCgpR3lxIkYsJCEzajdZdTxAWlA3Riw3JCQhMy8rdikpZiZHS2kiRiwkITNTI1IlR3IkcG1GIkYsNyQkITMhb21tc0NHJ1E6RiwkITN0JnBReGYlSEM4Riw3JCQhM0UkZVIob21VWzlGLCQhMzczalslMzlzUSJGLDckJCEzcSpcNy00RCNlOEYsJCEzQ1IvXy1XLG45Riw3JCQhMy5daTohKXkwOjhGLCQhM3hbSiJ6bzZJXiJGLDckJCEzTSsrNXExKj1GIkYsJCEzeWUwUGdzTmw6Riw3JCQhM21dUC9nTXNHN0YsJCEzIUgrP0Q5O2BpIkYsNyQkITMnNF0oKSpcaWImPSJGLCQhM1FuXTdzcF0lcCJGLDckJCEzdEQxXCg9biJSNkYsJCEzKVxgKkdkOmQieSJGLDckJCEzW11QKlw3eUY0IkYsJCEzeWIpR086V18pPUYsNyQkITMnR0pYUGYkZXA1RiwkITM0bkMoKVwiZVolPkYsNyQkITNDdm9caSEqUVk1RiwkITMmZS10YlApUTU/Riw3JCQhM2lQJVs3YCU+QjVGLCQhM3c0JUd2XHRJMyNGLDckJCEiIiIiISQhMyFIbFFQVGBSOyNGLC0lJkNPTE9SRzYmJSRSR0JHJCIjNUZoXWwkRmldbEZoXWxGYl5sLSUrQVhFU0xBQkVMU0c2JFEieDYiUSFGZ15sLSUlVklFV0c2JDskITErKysrKytTJiohIzokISM1RmhdbDskITEySVohPUtzPSNGX19sJCExI29sRzVqdHcqISM7LSUlRk9OVEc2JCUqSEVMVkVUSUNBR0ZhXmw=

plot(func2(z),z=start..ends);

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

series(f(x), x=0);

NiMrMUkieEc2IiIiIiIiISEiI0YmIiIlIiIjISIoIiIkIyIjUEYsRikjISMoKUYpIiImLUkiT0dJKnByb3RlY3RlZEdGNDYjRiYiIic=

taylor( f(x), x=0 );

NiMrMUkieEc2IiIiIiIiISEiI0YmIiIlIiIjISIoIiIkIyIjUEYsRikjISMoKUYpIiImLUkiT0dJKnByb3RlY3RlZEdGNDYjRiYiIic=

convert(taylor( f(x), x=0 ), polynom);

NiMsLiIiIkYkSSJ4RzYiISIjKiRGJSIiIyIiJSokRiUiIiQhIigqJEYlRiojIiNQRiwqJEYlIiImIyEjKClGKg==

M:=Matrix( [ [X[1],X[2],X[3]], [Y[1],Y[2],Y[3]],[X[2],X[2],X[3]] ]);

NiM+SSJNRzYiLUknUlRBQkxFR0YlNiUiKTciW0QjLUknTUFUUklYR0YlNiM3JTclJCErKysrMHUhIiokISsrKytxX0YxJCErKysrTkpGMTclJCErI0drLCsiRjEkIStVUiY+KyJGMSQhKzw6OUc1RjE3JUYyRjJGNEknTWF0cml4RzYkSSpwcm90ZWN0ZWRHRkBJKF9zeXNsaWJHRiU=

with (linalg);

Warning, the protected names norm and trace have been redefined and unprotected

NiM3XnJJLkJsb2NrRGlhZ29uYWxHNiJJLEdyYW1TY2htaWR0R0YlSSxKb3JkYW5CbG9ja0dGJUkpTFVkZWNvbXBHRiVJKVFSZGVjb21wR0YlSSpXcm9uc2tpYW5HRiVJJ2FkZGNvbEdGJUknYWRkcm93R0YlSSRhZGpHRiVJKGFkam9pbnRHRiVJJmFuZ2xlR0YlSShhdWdtZW50R0YlSShiYWNrc3ViR0YlSSViYW5kR0YlSSZiYXNpc0dGJUknYmV6b3V0R0YlSSxibG9ja21hdHJpeEdGJUkoY2hhcm1hdEdGJUkpY2hhcnBvbHlHRiVJKWNob2xlc2t5R0YlSSRjb2xHRiVJJ2NvbGRpbUdGJUkpY29sc3BhY2VHRiVJKGNvbHNwYW5HRiVJKmNvbXBhbmlvbkdGJUknY29uY2F0R0YlSSVjb25kR0YlSSljb3B5aW50b0dGJUkqY3Jvc3Nwcm9kR0YlSSVjdXJsR0YlSSlkZWZpbml0ZUdGJUkoZGVsY29sc0dGJUkoZGVscm93c0dGJUkkZGV0R0YlSSVkaWFnR0YlSShkaXZlcmdlR0YlSShkb3Rwcm9kR0YlSSplaWdlbnZhbHNHRiVJLGVpZ2VudmFsdWVzR0YlSS1laWdlbnZlY3RvcnNHRiVJK2VpZ2VudmVjdHNHRiVJLGVudGVybWF0cml4R0YlSSZlcXVhbEdGJUksZXhwb25lbnRpYWxHRiVJJ2V4dGVuZEdGJUksZmZnYXVzc2VsaW1HRiVJKmZpYm9uYWNjaUdGJUkrZm9yd2FyZHN1YkdGJUkqZnJvYmVuaXVzR0YlSSpnYXVzc2VsaW1HRiVJKmdhdXNzam9yZEdGJUkoZ2VuZXFuc0dGJUkqZ2VubWF0cml4R0YlSSVncmFkR0YlSSloYWRhbWFyZEdGJUkoaGVybWl0ZUdGJUkoaGVzc2lhbkdGJUkoaGlsYmVydEdGJUkraHRyYW5zcG9zZUdGJUkpaWhlcm1pdGVHRiVJKmluZGV4ZnVuY0dGJUkqaW5uZXJwcm9kR0YlSSlpbnRiYXNpc0dGJUkoaW52ZXJzZUdGJUknaXNtaXRoR0YlSSppc3NpbWlsYXJHRiVJJ2lzemVyb0dGJUkpamFjb2JpYW5HRiVJJ2pvcmRhbkdGJUkna2VybmVsR0YlSSpsYXBsYWNpYW5HRiVJKmxlYXN0c3Fyc0dGJUkpbGluc29sdmVHRiVJJ21hdGFkZEdGJUknbWF0cml4RzYkSSpwcm90ZWN0ZWRHRltwSShfc3lzbGliR0YlSSZtaW5vckdGJUkobWlucG9seUdGJUknbXVsY29sR0YlSSdtdWxyb3dHRiVJKW11bHRpcGx5R0YlSSVub3JtR0ZccEkqbm9ybWFsaXplR0YlSSpudWxsc3BhY2VHRiVJJ29ydGhvZ0dGJUkqcGVybWFuZW50R0YlSSZwaXZvdEdGJUkqcG90ZW50aWFsR0YlSStyYW5kbWF0cml4R0YlSStyYW5kdmVjdG9yR0YlSSVyYW5rR0YlSShyYXRmb3JtR0YlSSRyb3dHRiVJJ3Jvd2RpbUdGJUkpcm93c3BhY2VHRiVJKHJvd3NwYW5HRiVJJXJyZWZHRiVJKnNjYWxhcm11bEdGJUktc2luZ3VsYXJ2YWxzR0YlSSZzbWl0aEdGJUksc3RhY2ttYXRyaXhHRiVJKnN1Ym1hdHJpeEdGJUkqc3VidmVjdG9yR0YlSSlzdW1iYXNpc0dGJUkoc3dhcGNvbEdGJUkoc3dhcHJvd0dGJUkqc3lsdmVzdGVyR0YlSSl0b2VwbGl0ekdGJUkmdHJhY2VHRlxwSSp0cmFuc3Bvc2VHRiVJLHZhbmRlcm1vbmRlR0YlSSp2ZWNwb3RlbnRHRiVJKHZlY3RkaW1HRiVJJ3ZlY3RvckdGam9JKndyb25za2lhbkdGJQ==

det(M);

NiMkIipwejwnWyEiKQ==

diff(f(x),x);

NiMsJiomLCYtSSRleHBHNiRJKnByb3RlY3RlZEdGKUkoX3N5c2xpYkc2IjYjSSJ4R0YrIiIiISIiRi5GLiwmRiZGLkYtRi5GL0YuKigsJkYmRi5GLUYvRi5GMCEiIywmRiZGLkYuRi5GLkYv

int(f(x),x=-5..-1);

NiMtSSRpbnRHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkKiYsJi1JJGV4cEdGJTYjSSJ4R0YoIiIiRi8hIiJGMCwmRixGMEYvRjBGMS9GLzshIiZGMQ==

####### 3 ########A:=Matrix( [ [(S+b1), a6, b2, 0, 0], [b6, (S+a1), a2, 0, 0], [-b7, 0, -1, (S+a4), -b4, 0], [-1, 0, 0, S, 0], [0, -1, 0, 0, S] ]);

NiM+SSJBRzYiLUknUlRBQkxFR0YlNiUiKU8iNEwjLUknTUFUUklYR0YlNiM3JzcoLCZJIlNHRiUiIiJJI2IxR0YlRjFJI2E2R0YlSSNiMkdGJSIiIUY1RjU3KEkjYjZHRiUsJkYwRjFJI2ExR0YlRjFJI2EyR0YlRjVGNUY1NygsJEkjYjdHRiUhIiJGNUY+LCZGMEYxSSNhNEdGJUYxLCRJI2I0R0YlRj5GNTcoRj5GNUY1RjBGNUY1NyhGNUY+RjVGNUYwRjVJJ01hdHJpeEc2JEkqcHJvdGVjdGVkR0ZHSShfc3lzbGliR0Yl

B:=Matrix( [-a5, -b3], [-a3, -b5], [-a7, 0], [0,0], [0,0] );TTdSMApJNVJUQUJMRV9TQVZFLzIyNTQ4MTEyWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQkISsrKyswdSEiKiQhKyNHaywrIkYpJCErCisrK3FfRilGLCQhK1VSJj4rIkYpRiwkISsrKytOSkYpJCErPDo5RzVGKUYwRiYKTTdSMApJNVJUQUJMRV9TQVZFLzIzMzA5MTM2WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjPyImIicsJiUiU0ciIiIlI2IxR0YpJSNiNkcsJCUjCmI3RyEiIkYuIiIhJSNhNkcsJkYoRiklI2ExR0YpRi9GL0YuJSNiMkclI2EyR0YuRi9GL0YvRi8sJkYoRiklI2E0R0YpRihGL0YvRi8sJCUKI2I0R0YuRi9GKEYvRi9GL0YvRi9GJgo=