Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, a, u, v, w, x, y, z
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd
from proveit.logic import CartExp, Equals, InSet
from proveit.numbers import Real, three

# build up the expression from sub-expressions
sub_expr1 = ScalarMult(a, v)
sub_expr2 = CartExp(Real, three)
sub_expr3 = TensorProd(u, sub_expr1, VecAdd(w, x, y), z)
expr = ExprTuple(InSet(sub_expr3, TensorProd(sub_expr2, sub_expr2, sub_expr2, sub_expr2)), Equals(sub_expr3, VecAdd(TensorProd(u, sub_expr1, w, z), TensorProd(u, sub_expr1, x, z), TensorProd(u, sub_expr1, y, z))).with_wrapping_at(2))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(u {\otimes} \left(a \cdot v\right) {\otimes} \left(w + x + y\right) {\otimes} z\right) \in \left(\mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3} {\otimes} \mathbb{R}^{3}\right), \begin{array}{c} \begin{array}{l} \left(u {\otimes} \left(a \cdot v\right) {\otimes} \left(w + x + y\right) {\otimes} z\right) =  \\ \left(\left(u {\otimes} \left(a \cdot v\right) {\otimes} w {\otimes} z\right) + \left(u {\otimes} \left(a \cdot v\right) {\otimes} x {\otimes} z\right) + \left(u {\otimes} \left(a \cdot v\right) {\otimes} y {\otimes} z\right)\right) \end{array} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	8, 7
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 24 operands: 10
8	Operation	operator: 24 operands: 11
9	Operation	operator: 20 operands: 12
10	ExprTuple	13, 13, 13, 13
11	ExprTuple	30, 31, 14, 33
12	ExprTuple	15, 16, 17
13	Operation	operator: 18 operands: 19
14	Operation	operator: 20 operands: 21
15	Operation	operator: 24 operands: 22
16	Operation	operator: 24 operands: 23
17	Operation	operator: 24 operands: 25
18	Literal
19	ExprTuple	26, 27
20	Literal
21	ExprTuple	28, 29, 32
22	ExprTuple	30, 31, 28, 33
23	ExprTuple	30, 31, 29, 33
24	Literal
25	ExprTuple	30, 31, 32, 33
26	Literal
27	Literal
28	Variable
29	Variable
30	Variable
31	Operation	operator: 34 operands: 35
32	Variable
33	Variable
34	Literal
35	ExprTuple	36, 37
36	Variable
37	Variable