an interview notebook!

interview_kernel/interview_kernel/example_interview.ipynb

+%% Cell type:code id: tags:
+
+``` text
+anything
+```
+
+%%%% Output: stream
+
+    Hello, user! I am TheInterview, your partial differential equations and simulations expert. Let's set up a simulation together.
+    How many dimensions does your model have?
+    I am just assuming it's 1, since that is all we can currently handle.
+    
+    
+    What is the domain you would like to simulate for?     Ω : type ❘ = [?;?], e.g. Ω = [0.0;1.0]
+    By the way, you can always try and use LaTeX-type input.
+
+%% Cell type:code id: tags:
+
+``` text
+Ω = [0.0;1.0]
+```
+
+%%%% Output: stream
+
+    we will just assume that the variable is called x for now.
+    
+    
+    Which variable(s) are you looking for? / What are the unknowns in your model?  u : Ω → ??,  e.g., u : Ω → ℝ ?
+
+%% Cell type:code id: tags:
+
+``` text
+u : Ω → ℝ
+```
+
+%%%% Output: stream
+
+    Ok, u : Ω → ℝ
+    u : Ω → ℝ
+    
+    
+    Would you like to name additional parameters like constants or functions (that are independent of your unknowns)?  c : ℝ = ? or f : Ω → ℝ = ?
+
+%% Cell type:code id: tags:
+
+``` text
+f = x
+```
+
+%%%% Output: stream
+
+    Ok, f = [ x : Ω] x
+    Would you like to declare more parameters? [y/n]?
+
+%% Cell type:code id: tags:
+
+``` text
+y
+```
+
+%%%% Output: stream
+
+
+%% Cell type:code id: tags:
+
+``` text
+\alpha = -5.0
+```
+
+%%%% Output: stream
+
+    Ok, α = [ x : Ω] -5.0
+    Would you like to declare more parameters? [y/n]?
+
+%% Cell type:code id: tags:
+
+``` text
+y
+```
+
+%%%% Output: stream
+
+
+%% Cell type:code id: tags:
+
+``` text
+k = x \cdot x
+```
+
+%%%% Output: stream
+
+    I did not catch that. Could you please rephrase?
+    Details: MMT server error: unbound token: ·
+
+%% Cell type:code id: tags:
+
+``` text
+n
+```
+
+%%%% Output: stream
+
+    f = x
+    α = -5.0
+    
+    
+    Let's talk about your partial differential equation(s). What do they look like? Δu = 0.0, or laplace_operator Ω ℝ u = f ?
+
+%% Cell type:code id: tags:
+
+``` text
+Δu = \alpha
+```
+
+%%%% Output: stream
+
+    Ok, <result>
+      <xml>
+        <theory meta="http://mathhub.info/MitM/Foundation?Logic" base="http://mathhub.info/MitM/smglom/calculus" name="ephpde1">
+    
+    
+            <import from="http://mathhub.info/MitM/smglom/calculus?mDifferentialOperators"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#0.0.0:32.0.32" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata></import><import from="http://mathhub.info/MitM/smglom/calculus?u"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#0.0.0:11.0.11" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata></import><import from="http://mathhub.info/MitM/smglom/calculus?f"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#0.0.0:11.0.11" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata></import><import from="http://mathhub.info/MitM/smglom/calculus?&#945;"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#0.0.0:11.0.11" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata></import><constant name="mylhs">
+           <metadata><link resource="http://mathhub.info/MitM/smglom/calculus#1.0.1:35.0.35" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata>
+           <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
+                     <om:OMS name="Pi" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
+                     <om:OMBVAR><om:OMV name="anyu"><type><om:OMA><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#19.0.19:23.0.23" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata>
+                  <om:OMS name="arrow" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
+                  <om:OMS name="&#937;" module="ephdomain" base="http://mathhub.info/MitM/smglom/calculus"/><om:OMS name="real_lit" module="RealLiterals" base="http://mathhub.info/MitM/Foundation"/>
+          </om:OMA></type></om:OMV></om:OMBVAR>
+                     <om:OMA>
+                  <om:OMS name="arrow" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
+                  <om:OMS name="&#937;" module="ephdomain" base="http://mathhub.info/MitM/smglom/calculus"/><om:OMS name="real_lit" module="RealLiterals" base="http://mathhub.info/MitM/Foundation"/>
+          </om:OMA>
+          </om:OMBIND></om:OMOBJ></type>
+           <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#10.0.10:32.0.32" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata>
+                     <om:OMS name="lambda" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
+                     <om:OMBVAR><om:OMV name="anyu"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#12.0.12:15.0.15" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata><type><om:OMA><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#19.0.19:23.0.23" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata>
+                  <om:OMS name="arrow" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
+                  <om:OMS name="&#937;" module="ephdomain" base="http://mathhub.info/MitM/smglom/calculus"/><om:OMS name="real_lit" module="RealLiterals" base="http://mathhub.info/MitM/Foundation"/>
+          </om:OMA></type></om:OMV></om:OMBVAR>
+                     <om:OMA><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#27.0.27:32.0.32" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata>
+                  <om:OMS name="apply" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
+                  <om:OMS name="laplace_operator" module="mDifferentialOperators" base="http://mathhub.info/MitM/smglom/calculus"/><om:OMS name="&#937;" module="ephdomain" base="http://mathhub.info/MitM/smglom/calculus"/><om:OMS name="real_lit" module="RealLiterals" base="http://mathhub.info/MitM/Foundation"/><om:OMV name="anyu"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#29.0.29:32.0.32" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata></om:OMV>
+          </om:OMA>
+          </om:OMBIND></om:OMOBJ></definition>
+    
+         </constant><constant name="myrhs">
+           <metadata><link resource="http://mathhub.info/MitM/smglom/calculus#1.0.1:12.0.12" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata>
+           <type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMBIND>
+                     <om:OMS name="Pi" module="LambdaPi" base="http://cds.omdoc.org/urtheories"/>
+                     <om:OMBVAR><om:OMV name="x"><type><om:OMS name="&#937;" module="ephdomain" base="http://mathhub.info/MitM/smglom/calculus"/></type></om:OMV></om:OMBVAR>
+                     <om:OMS name="real_lit" module="RealLiterals" base="http://mathhub.info/MitM/Foundation"/>
+          </om:OMBIND></om:OMOBJ></type>
+           <definition><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS name="&#945;" module="&#945;" base="http://mathhub.info/MitM/smglom/calculus"><metadata><link resource="http://mathhub.info/MitM/smglom/calculus#10.0.10:10.0.10" rel="http://cds.omdoc.org/mmt?metadata?sourceRef"/></metadata></om:OMS></om:OMOBJ></definition>
+    
+         </constant>
+          </theory>
+      </xml>
+    </result>
+    
+    
+    
+    These are all the PDEs needed.
+    Let's discuss your boundary conditions. What do they look like? u(x) = f(x) or u(1.0) = \alpha ?
+
+%% Cell type:code id: tags:
+
+``` text
+u = f
+```
+
+%%%% Output: stream
+
+    Ok
+    
+    
+    These are all the boundary conditions needed.
+    Would you like to try and solve the PDE using the Finite Difference Method in ExaStencils? [y/n]?
+
+%% Cell type:code id: tags:
+
+``` text
+y
+```
+
+%%%% Output: stream
+
+    Generated ExaStencils input.
+
+%% Cell type:code id: tags:
+
+``` text
+```