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Expression of type InSet

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import l
from proveit.logic import InSet
from proveit.numbers import Abs, IntervalOC, Mult, frac, pi, subtract, two, zero
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = InSet(Mult(pi, Abs(subtract(_delta_b_floor, frac(l, _two_pow_t)))), IntervalOC(zero, frac(pi, two)))
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(\pi \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right|\right) \in \left(0,\frac{\pi}{2}\right]
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple16, 9
7Literal
8ExprTuple10, 11
9Operationoperator: 12
operand: 15
10Literal
11Operationoperator: 27
operands: 14
12Literal
13ExprTuple15
14ExprTuple16, 33
15Operationoperator: 17
operands: 18
16Literal
17Literal
18ExprTuple19, 20
19Operationoperator: 21
operand: 25
20Operationoperator: 23
operand: 26
21Literal
22ExprTuple25
23Literal
24ExprTuple26
25Literal
26Operationoperator: 27
operands: 28
27Literal
28ExprTuple29, 30
29Variable
30Operationoperator: 31
operands: 32
31Literal
32ExprTuple33, 34
33Literal
34Literal