Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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
from proveit.numbers import Add, Exp, Mult, frac, one, subtract, three, two
from proveit.physics.quantum.QPE import _eps

# build up the expression from sub-expressions
sub_expr1 = frac(one, _eps)
sub_expr2 = Mult(Exp(_eps, subtract(two, one)), Add(three, sub_expr1))
sub_expr3 = Mult(Exp(_eps, two), Exp(Add(two, sub_expr1), two))
expr = ExprTuple(frac(Mult(_eps, sub_expr2), sub_expr3), Mult(_eps, frac(sub_expr2, sub_expr3)))

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(\frac{\epsilon \cdot \left(\epsilon^{2 - 1} \cdot \left(3 + \frac{1}{\epsilon}\right)\right)}{\epsilon^{2} \cdot \left(2 + \frac{1}{\epsilon}\right)^{2}}, \epsilon \cdot \frac{\epsilon^{2 - 1} \cdot \left(3 + \frac{1}{\epsilon}\right)}{\epsilon^{2} \cdot \left(2 + \frac{1}{\epsilon}\right)^{2}}\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: 34 operands: 3
2	Operation	operator: 12 operands: 4
3	ExprTuple	5, 10
4	ExprTuple	37, 6
5	Operation	operator: 12 operands: 7
6	Operation	operator: 34 operands: 8
7	ExprTuple	37, 9
8	ExprTuple	9, 10
9	Operation	operator: 12 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 21 operands: 18
15	Operation	operator: 27 operands: 19
16	Operation	operator: 21 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprTuple	37, 23
19	ExprTuple	24, 31
20	ExprTuple	37, 30
21	Literal
22	ExprTuple	25, 30
23	Operation	operator: 27 operands: 26
24	Literal
25	Operation	operator: 27 operands: 28
26	ExprTuple	30, 29
27	Literal
28	ExprTuple	30, 31
29	Operation	operator: 32 operand: 36
30	Literal
31	Operation	operator: 34 operands: 35
32	Literal
33	ExprTuple	36
34	Literal
35	ExprTuple	36, 37
36	Literal
37	Literal