# from the theory of proveit.physics.quantum.QPE¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import ExprTuple, e
from proveit.numbers import Add, LessEq, Neg, one
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(LessEq(sub_expr2, sub_expr2), LessEq(sub_expr2, sub_expr1), LessEq(sub_expr1, _two_pow__t_minus_one))

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(-2^{t - 1} + 1\right) \leq \left(-2^{t - 1} + 1\right), \left(-2^{t - 1} + 1\right) \leq \left(-\left(e + 1\right)\right), \left(-\left(e + 1\right)\right) \leq 2^{t - 1}\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2, 3
1Operationoperator: 6
operands: 4
2Operationoperator: 6
operands: 5
3Operationoperator: 6
operands: 7
4ExprTuple8, 8
5ExprTuple8, 9
6Literal
7ExprTuple9, 16
8Operationoperator: 22
operands: 10
9Operationoperator: 26
operand: 13
10ExprTuple12, 28
11ExprTuple13
12Operationoperator: 26
operand: 16
13Operationoperator: 22
operands: 15
14ExprTuple16
15ExprTuple17, 28
16Operationoperator: 18
operands: 19
17Variable
18Literal
19ExprTuple20, 21
20Literal
21Operationoperator: 22
operands: 23
22Literal
23ExprTuple24, 25
24Literal
25Operationoperator: 26
operand: 28
26Literal
27ExprTuple28
28Literal